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Integrate \int (e^-xy)*sin(x) step-by-step Found solution for e^x*sin(x). It used integration by parts. Tried it here but keep getting too many Ys.

Welcome to Math.SE, jdash. This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 21 secs ago
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Related to this similar problem. I am attempting to solve the following: Find a natural cubic spline function whose knots are $-1$, $0$, and $1$ and that takes on the values $S(-1)=5$, $S(0)=7$, and $S(1)=9$. Neither my textbook nor my class notes have been particularly helpful in showing ...

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I am trying to implement an algorithm described in a paper. At one point, it says "Let $\phi_0,\phi_1,\ldots$ be a collection of functions from $\mathbb{R}^d$ to $\mathbb{R}$ such that $\phi_0\equiv1$ and $\{\phi_i(X_t)\}$ form a basis for $L^2(\Omega,\sigma(X_t),\mathbb{Q})$ for all $t=1,\ldot... 0 Pick a sequence of 10 balls from a sack containing red, blue, green, yellow, white and black balls. Each time a ball is picked, it is replaced in the sack before the next ball is picked. a) How many sequences have exactly 3 balls? b) At least 4 blue balls? c) exactly 2 black balls AND at ... 0 Are there rules for higher powers? It seems like even and odd is preserved by powers, but how do I prove that? 0 I'm trying to solve this with two methods. P(Min of 3 Dice Rolls < 3) = P(D1 < 3 U D2 < 3 U D3 < 3) = 1 - P(D1 >= 3 n D2 >=3 n D3 >=3) For the union probability I'm getting .7 repeating, while for the intersection probability I'm getting .703 repeating. Can someone show me both methods are ... 0 Problem: Show that the set of polynomials with rational coefficients is countable. Idea: We know that the set of rational numbers is denumerable. This implies that the set of rational numbers is countable. We also know that the degree that each polynomial can be is a natural number (I think, an... 0 If i'm given 3 distinct points (a, b, and c) how would i describe the set of all points (d) in which abcd is a cyclic quadrilateral? I'm thinking that it is any point on the circle which contains triangle abc with exception of the vertices of said triangle. Is this correct? Short title. Cyclic Quadrilateral 0 Problem: Suppose that there is a function mapping S onto T. Prove that Card(S) is greater than or equal to Card(T). Issue: I can't seem to find a reason why this follows. If S is onto T then this guarantees that for any element in T there is at least one element in S. Therefore, I keep coming u... 0 A 10 foot high tank shaped like an inverted pyramid with a square base measuring 16ft by 16ft is filling with water at a rate of 2.5 cubic feet per a second. How fast is the water rising when the water is 8 feet high. Short title. Title contains problem. Calculus word problem 0 John is building a rectangular pen against his garage using wooden fencing. He wants to divide it further into 4 smaller pens all of equal size by placing 2 perpendicular units of fencing in the middle. John has 100 feet of fencing and wants to make the pen as big as possible. Find both the dimen... Short title. Title contains problem. Calculus optimization problem 12:59 AM 0 I posted a comment on this question thinking Programmers.SE would be a better fit for it. Apparently I was wrong, and two other commenters explained why. But my comment was also deleted, and now the other two folks' comments are out of context. Who deleted my comment? Why? Why wasn't I notifie... 0 Let$K$be a number field,$\mathcal{O}_k$its ring of integers,$\operatorname{Cl}(K)$its class group and$h_K = \lvert \operatorname{Cl}(K)\rvert$its class number. Let$X = \operatorname{Spec}(\mathcal{O}_K)$and let$U\subseteq X$be an open subset of$X$. Apparently (ex.3.19 Liu), using the... 0 I tried to prove this by contradiction and what I did is. I used contradiction proof that is n is odd then 5n^2 - 3 is even. But my Professor said this is wrong you need to prove that 5n^2 - 3 is even then n is odd. Can someone help me please? Welcome to Math.SE, Mitch. Tag (proof-verification) should not be the only tag a question has. Please add a tag for a subject area to which the question belongs. (from a bot)Normal Human 21 secs ago 0 Sample deviation is calculated as population standard deviation/sqrt(sample size) σ/√(n). Then why in an example like this below, is the answer 5.086? I understand that it comes from 4.2+1.96*1.5/sqrt(11), but why are we dividing with sqrt(11) when going from sample to population, when according ... Welcome to Math.SE, Frasier. Words such as question do not add information to titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 21 secs ago 0 Let f(x)=x^2+1/x^2-9 So to find the y intercept I take f(0) correct? So when I substitute 0 for x I got -1/9 so is the y intercept (0,-1/9) Also to find the x intercept I set the numerator equal to 0. So then I got x^2+1=0 but wouldn't that make x^2=-1 which is imaginary? I'm a little confused ... This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 21 secs ago 0 I would like to stress the kind of reference I am looking for... In statistics there are lots of motivating (and sometimes unexpected) examples that are interested for everyone such as Birthday Problem, Simpson Paradox, secretary problem, St Petersburg Paradox that easily motivate people from dif... 0 Let be$C_n$the rectangle, positively oriented, which sides are in the lines $$x=\pm(N+\dfrac{1}{2})\pi~~~y=\pm(N+\dfrac{1}{2})\pi$$ with$N\in\mathbb{N}$. Prove that $$\displaystyle\int_{C_N} \dfrac{dz}{z^2\sin(z)}=2\pi i\left[ \frac{1}{6}+2\sum_{n=0}^\infty \dfrac{(-1)^n}{n^2\pi^2}\ri... Tall formulas in titles break the layout of question lists. Please replace \dfrac with \frac, remove \displaystyle in the title. (autocomment)Normal Human 21 secs ago 1:18 AM 1 I have noticed now that when you mark a question as a duplicate, a comment is automatically added in the nature of: Possible Duplicate [Question Title of Duplicate Goes Here] I have also noticed that if you go through the flag menu and mark the question as duplicate of the same question the... 0 How to prove the Schwartz function in \mathbb{R}^n is dense in the space W^{2,p}(\mathbb{R}^n)? 0 How I calculate this integral using contour integration? \int_0^\pi \frac{3cos(n\theta)}{5+4cos(n\theta)}d\theta I know I can start by using that cos(n\theta) = Re (e^{in\theta}), but I get bogged down in the computing. 0 Let E/F be a field extension. (a) If (E : F) = 2, is E/F a Galois extension? Justify your answer. (b) If (E : F) = 3, is E/F a Galois extension? Justify your answer. 0 I found the following in Baby Rudin: Theorem If x,y\in \Bbb R, x>0 then there exists a natural number n such that$$nx>y$$After this, he proves another theorem using the following Let x<y, we have y-x>0 then the theorem above yields that a natural number n exists such ... 0 Prove that for all positive x,y,z, (2e^x+\dfrac{2}{e^x})(2e^y+\dfrac{2}{e^y})(2e^z+\dfrac{2}{e^z}) \geq 64 I dont have that much experience with inequalities but I know I can rewrite 64 as 4^3 So here is my approach, if I can maybe prove that (2e^x+\dfrac{2}{e^x}) \geq4 as well for ... Welcome to Math.SE, Joshua. Tall formulas in titles break the layout of question lists. Please replace \dfrac with \frac in the title. (from a bot)Normal Human 21 secs ago 0 Instinctively I think yes, since a = k + b for all a and b, but then I think about, eg. 4 congruent to 7 (modulo 1) and I'm confused about what the least residue of that would be... 0 I am trying to show that$$\sum_{i=1}^{100}(n+i)^{n+i}\equiv 0 mod 100$$Any tips? 0 I don't know weak derivative of 1/r^n where r is norm of x. (i.e. distance of from origin to x) If n=1, it's easy by logarithm and integration by parts because log(x) is locally integrable. but if n>1, how to approach to it? 0 Double Integral Problem I just don't understand how to do the last step and calculate the actual value with the integral with respect to y. Any help is appreciated. Thank you so much! 0 What is the expected number of tosses of fair coin to get THH? Here's my approach: Let N := number of tosses to get THH. Then by partitioning the sample space,$$ E(N) = E(N; H) + E(N; T). $$If we get a H on the first toss (with probability \frac{1}{2}) then we basically start over... 0 THis is an exercise on Martin Braun's Differential Equations and Their Applications p.544 Exercise 5. Let P_n(x) be the Legendre polynomial of degree n. (a) Show that P_n'(x) satisfies a selfadjoint equation with \lambda = n(n+1) - 2 (b) Show that \int_{-1}^1 P_n'(x) P_m'(x) (1-x^2)dx ... Welcome to Math.SE, ODE learner. Words such as question are uninformative in titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (from a bot)Normal Human 21 secs ago 0 I'm trying to think of functions that are injective but not surjective. I can think of f(x) = e^x for f: R --> R (since the range should be positive R for this to be surjective, but R+ is a subset of R) and f(a,b) = a^b for f: ZxZ --> R (the range should be Q for this to be surjective, but Q is a... Questions tend to get more attention when they have a tag for a broad area of mathematics relevant to the question. Some of these tags might fit. (from a bot)Normal Human 21 secs ago 0 A is a 2x5 matrix with two pivot positions. Does the equation Ax=b have at least one solution for every possible b? If the answer is yes, then I understand why. If the answer is no, please explain. Welcome to Math.SE, Muuz. Words such as question are uninformative in titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (autocomment)Normal Human 21 secs ago 0 The problem said: Let X and Y be identically distributed independent random variables such that the moment generating function of X + Y is M(t) = 0.09e 2t + 0.24e t + 0.34 + 0.24et + 0.09e2t, −1 < t < 1 Calculate P(X <=0). I found the path to have the correct answer: We must just b... This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 21 secs ago 0 I want to prove the following: Let K be a field, let g(X) \in K[X] be an irreducible polynomial, and let L be a splitting field for g(X) over K. Prove that g(X) has at least one repeated root in L if and only if char(K) = p for some p > 0 and g(X) = h(X^p) for some h(X) \i... Title contains exercise. An exercise about repeated root 0 Let f be a given continuous function on [0,1]. Prove that there is a unique continuous function g on [0,1] satisfying$$g(x) = \frac{1}{2}g\left(\frac{x+1}{2}\right) + f(x)$$for all x in [0,1]. Welcome to Math.SE, user298514. Consider replacing (analysis) with a more specific tag for the relevant branch of analysis. (from a bot)Normal Human 21 secs ago 0 X_1,X_2,...,X_n\;i.i.d\;with bernoulli distribution(p.m.f is \theta^{x}(1-\theta)^{1-x}). I want to gain distribution of \bar X. Then I calculated moment generating function of \bar X(by calculating E[e^{\frac t n (X_1+...+X_n)}]. And I gained M.G.F of \bar X. Result is (1-\theta... 2:44 AM 0 A paperweight has a slanted top described by x + y + z = 2. Its edges are orthogonal to the xy–plane, and the bottom of the paperweight is formed by the triangle with vertices (1, 0, 0),(0, −1, 0) and (0, 1, 0). Use a triple integral to find the volume of the paperweigh. From the base of the gra... 0 I love hats too, but this user loves hats way too much: In the past 10 minutes they edited 5 old posts, probably for a hat :D Each one of these posts only add a few back-ticks. Is this something that these hats are encouraging? 3:00 AM 0 isomorphic copies of V, where V = k^n. I was able to show that R has a unique simple module V, but I'm stuck on the rest of the exercise. Any help is appreciated. 0 Sketch the graph of the function y=x(4-x)-83lnx. Indicate the transition points (local extrema and points of inflection). Local minimum x= Local maximum x= inflection at x= I understand how to solve this problem mathematically, however, is there any way of analyzing the question to get a better... 0 Hi I was checking my answers with my professor and I think the way he solved it was wrong can you please check? Question: Let R be the region in the xy-plane bounded by the axes and the line x + y = 1. Use the change-of-variable transformation T(u, v) = (u + v,u v) to evaluate, ZZ R(x y)5(x + y)... This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 20 secs ago 0 If u_k\rightharpoonup u weakly in W^{1,q}(U),how to show$$ \sup\limits_{k}||u_k||_{W^{1.q}(U)}<\infty $$Title contains \limits. Short question. How to show \sup\limits_{k}||u_k||_{W^{1.q}(U)}<\infty ? 0 Consider the functions f(x)=(x^2-14x+49) and g(x)=(x-7) and f(x)/g(x)=(x^2-14x+49)/(x-7), notice how f is g^2 because you can factor (x^2-14x+49)=(x-7)^2 so f/g = (x-7)^2/(x-7) = (x-7). So since f/g = (x-7) which is just a line the domain should just be (-infinity, infinity) right? But here is wh... Welcome to Math.SE, user273872. This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 20 secs ago 0 I would like a verification of a proof for the following statement. Let S be a multiplicatively closed subset of a ring R. If R is a PID, then S^{-1}R is a PID. Let I = \left<r_1/s_1, r_2/s_2\ldots\right> be an ideal of S^{-1}R. Since 1/s_i is a unit in S^{-1}R, we have \left<r_... Tagged proof-verification. Localization of a PID is a PID 3:28 AM 0$$\int\int_D 6x\sqrt{y^2-x^2}dA, D=\{(x,y)|0\leq y\leq 2, 0 \leq x \leq y\}$$I tried:$$\int_0^2 \int_0^y 6x\sqrt{y^2-x^2}dxdy$$But that is incorrect. 0 Let Au_i=u_{i+1}-(2-\beta)u_i+u_{i-1} whith u\in \ell^2=\{(u_i)_{i\in Z}:\sum_{i\in Z}u_i<+\infty\}. How to compute ||A^{-1}|| or estimate it?? Is it a sectorial operator of type (\omega, \theta) with \omega <0???? Welcome to Math.SE, Nguyen Nhu Quan. Words such as question, please, help do not add information to titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (from a bot)Normal Human 20 secs ago 0 How come in u-substitution if u is to the -1 power it becomes equivalent to the ln of u? I don't have a specific problem where that is the case , however I do recall this being a rule of thumb. Can someone explain this to me? 0 Let f : A \rightarrow B. Prove that if X \subseteq A, Y \subseteq B, and f is a bijection, then f(X) = Y if and only if f^{-1}(Y) = X. Short title. Title contains problem. Short question. Tagged proof-writing. Proofs problem with bijection 0 C=a∨b∨c∨d∨e is a clause in SAT D= (a∨b∨x)∧ (¯x∨c∨y)∧ (¯y∨d∨e) is the another form of C to make sure every clause has only threeliterals Is D true when C is true and false when C is false? Why? I think when a,x,y=true and b,c,d,e=false, then C is true but D is false. 0 As the title says I'm looking for Math textbooks whose copyright has expired or have an open source / creative commons compatible copyright. Tag (reference-request) should not be the only tag a question has. Please add a tag for a subject area to which the question belongs. (from a bot)Normal Human 20 secs ago 0 Consider$$\begin{bmatrix} C_{11}&C_{12}&\dots&C_{1n}\\ C_{21}&C_{22}&\dots&C_{2n}\\ \vdots\\ C_{n1}&C_{n2}&\dots&C_{nn}\\ D_{11}&D_{12}&\dots&D_{1n}\\ D_{21}&D_{22}&\dots&D_{2n}\\ \vdots\\ D_{n1}&D_{n2}&\dots&D_{nn}\\ \end{bmatrix}$$where each C_{ij} and D_{ij} is 1\times n submatrix. ... 0 Picture Link Here If someone could please explain in English what the question is actually asking, that'd be great. An explanation would be nice too, but no worries. (I know the answer is e, it's not homework) Title contains help, tricky. Question contains please. Tricky Linear Algebra syntax -- help me read it? Pic attached 0 The problem is Kreyszig 10ed international edition : 16.2 #9. What is the order of pole at z=\pi of the function f(z) below?$$f(z)=\frac{\sin z}{z-\pi}$$I thought that it will be simple pole because \sin z is analytic for all z$$\in$$\Bbb C and z-\pi has a 1st order zero at z=\pi.... Questions tend to get more attention when they have a tag for a broad area of mathematics relevant to the question. Some of these tags might fit. (from a bot)Normal Human 21 secs ago 0 If f(x) = (x+x) and g(x) = (x-5)*2, and we have the compound function g(f(x)), how can we "define what the resulting function does"? It's obvious what is happening, but I'm not quite sure how this question is asking and how it would be laid out. Perhaps, g(x) = ((x+x)-5)*2 4:23 AM 0 if f is a unitary matrix representation, then f is a equivalent to a direct sum of irreducible unitary representation via an equivalence implemented by a unitary matrix T. 0 If$$\frac{1}{\sigma_\widehat{e}^2}=\sum_i\frac{1}{\sigma_i^2}\tag{1}$$Pick anyone of the \sigma_j and multiply both sides of (1) by \sigma_j^2$$\implies\frac{\sigma_j^2}{\sigma_\widehat e^2}=\color{red}{\fbox{$\sum_i\frac{\sigma_j^2}{\sigma_i^2}=\color{blue}{1}+\sum_{i\ne j}\frac{\sigm...

Words such as question do not add information to titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (autocomment)Normal Human 21 secs ago
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I was learning (practicing to solve) simplifying the rational expressions. I know how to simplify the rational expressions... but I can't understand some part of the questions. The question that I can't understand If you look at this image, you could see sentence "First, let's set the denominat...

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Let A={x∈R, x not equal 1} B={x∈R, x not equal 2} f(x)=2x/(x-1) A -> B How to find the bijective of f(x)?

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Пока выборы не начались, хорошо бы исправить ошибки на странице выборов. http://ru.stackoverflow.com/election/1 Полужирным выделил необходимые правки. Модераторы нашего сообщества должны: быть терпеливыми и честными подавать личный пример демонстрировать уважение к другим участникам сообщест...

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How do I get secret hats in winter bash 2015? I wonder if I could wear as many as hats I get

4:47 AM
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What are the differences between a so called mathematical law and axiom? Please define both concepts in your answer.

Tag (definition) should not be the only tag a question has. Please add a tag for a subject area to which the question belongs. (autocomment)Normal Human 21 secs ago
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Are there better alternative definitions than $\exp(x) = {\large\sum\limits_{k=0}^\infty} \dfrac{x^k}{k!} , \ln(x) = {\large\int_1^x} \dfrac1t\ dt$. that can be used for derivation of their identities e.g. $\exp (x+y)=\exp(x)\exp(y)$, $\ln (xy) =\ln (x)\ln(y)$ ( and by extension sin and cos rela...

Tag (definition) should not be the only tag a question has. Please add a tag for a subject area to which the question belongs. (autocomment)Normal Human 21 secs ago
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If E/F is a field extension and (E:F)=2, is it Galois? What if (E:F)=3? I don't see why the degree of the field extension matter if it is finite. Thanks!

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Consider the following informal definition for a function calc(x,y) = (0*y) + (1*y) + … + (x*y) For example, we have that calc(2,5) = (0*5) + (1*5) + (2*5) Give a recursive definition for the function calc. Give a trace to show each step involved in calculating calc(3,4) using your def...

This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 21 secs ago

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I got a new notification You earned Sufganiyot on Web Application!. What is this Hat? You can see in my profile picture I wore this. Can anyone give a brief information about this?

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How to solve this differential equation:$$Ri(t)+ L\frac{di}{dt}= A\cos(\omega t+ \alpha)\;?$$ Any hint would be appreciated.

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Given an optimization as follows: \begin{align} \text{minimize}\quad &c^Tx \\ \text{subject to}\quad &Ax = 0 \\ & \|x\|_2^2 \leq 1 \end{align} where $A \in \Re^{m\times n}$ and $c \in \Re^n$. Let $x^*$ be the optimal solution to this problem. Because $c^Tx$, $\|x\|_2^2 - 1$ are convex and...

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If I'm given 3 vertices, say (5,3), (9,3), and (9,7), how can I draw this triangle in a 2 dimensional way along 2 axises and still represent it as a poincare triangle?

Welcome to Math.SE, addddddc. Words such as question are uninformative in titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (from a bot)Normal Human 21 secs ago
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$T\begin{bmatrix}a\\b\\c\\d\end{bmatrix} = 2a-3b+c-2d$ $v_1=\begin{bmatrix}1\\2\\3\\4\end{bmatrix}$ $v_2=\begin{bmatrix}1&2&3&4\end{bmatrix}$ then $T(v_1) = -9$ or $\begin{bmatrix}2\\-6\\3\\-8\end{bmatrix}$? then would $T(v_2) = -9$ or $\begin{bmatrix}2&-6&3&-8\end{bmatrix}$ or what?

Words such as question do not add information to titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (autocomment)Normal Human 21 secs ago
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Few days back one of my friend and I were discussing about Galois life and his ideas. Though we are not trained in Galois theory, but I am recently started to learn it by myself and hope to take up research on it some times soon. So I am wondering about the open problems in Galois theory? Is ther...

Title contains problem. Question contains please. What are some major open problems in Galois theory?
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Is it true that the equation $27x^2+1=7^3y^2$ has infinitely many solutions in positive integers $x,y$ ?

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$\lim_{x\rightarrow 0 } \dfrac{1}{x} \int_{x}^{2x} e^{-t^2} dx$ I dont have any idea to solve this integral ?

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The two ends of the frastum are circles with radii of 3cm and 9cm. Find the volume of the frastum. How to do the question?

5:30 AM
@NormalHuman: Not joining in this time?

@MikeMiller Correct. Real life's been busier than last year, so I withdrew from some aspects of SE.
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Brian Lara, the famous batsman, scored 6,000 runs in certain number of innings. In the next five innings he was out of form and hence, could make only a total of 90 runs, as a result of which his average fell by 2 runs. How many innings did he play in all, if he gets out in all the innings? (a)...

Welcome to Math.SE, Suyog. Words such as question are uninformative in titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (from a bot)Normal Human 22 secs ago

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I want your opinions on how useful it is to throw second quantization at students when they have not understood first quantization. I tend to add a simpler answer when I see this. Also the emphasis on second quantization and statements of the type "all space is filled with electron fields /parti...

Fair enough. I appreciate the comment bot, by the way.

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I'm trying to prove $\Box A\rightarrow \Box\Box A$ from $KG_r$ where $KG_r$ is the axiom $$\Box[ \Box A \rightarrow A ] \rightarrow \Box A$$ I'm given the hint that $$A \rightarrow ((\Box\Box A\land \Box A) \rightarrow (\Box A \land A))$$ is a theorem. I know that in any normal system you...

Questions tend to get more attention when they have a tag for a broad area of mathematics relevant to the question. Some of these tags might fit. (from a bot)Normal Human 20 secs ago
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Theorem: Let A and B be sets such that A$\cup$B≠B and B\A={}. Then we have that B$\subset$A Theorem is True. A and B are not identical sets. A contains all of B's elements, therefore B is a subset of A. Is this correct?

Short title. Tagged proof-theory. Set Theory Proof Verification

5:54 AM
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Having only Windows Phone as mobile operating system I won't be able to earn any of these two hats: Wireless nor Field Work Is it possible to know when will you guys stop undervaluing the Windows Universal Platform and start working on an app for it? It isn't that hard you know.

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The population of an ant colony doubles every day and a half. A biologist predicts the ant colony will eventually overtake a flower bed. What is the number of hours between the time the flower bed is half full and the time the flowerbed is completely full? Explain.

Welcome to Math.SE, user298555. Words such as question are uninformative in titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (autocomment)Normal Human 21 secs ago
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What is the value of $\dfrac{1}{1!} + \dfrac{1+2}{2!} + \dfrac{1+2+3}{3!} + \dots$ How to proceed with it ?

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G(x,t) =\begin{cases} a+ b(logt) & \text{if $0<x<t$ } \\[2ex] c+ d(logt) & \text{if $t<x<1$ } \end{cases} is a Greens function for $xy''+y'=0$ subject to y being bounded as x tends to $0$ and $y(1)=y'(1)$ if a) a=b=c=d=1 b)a=c=1,b=d=0 c)a=c=0,b=d=1 d)a=b=c=d=0 I don't know how to tackle th...

6:18 AM
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We are given initially some $k,c,d\in\mathbb{N}$. How many solutions $(x_1, x_2, ..., x_k)$ does the equation $\sum_{i=1}^{k}{x_i}=c$ have, where $x_i\in\mathbb{Z}$ and $0\leq x_i\leq d$?

6:29 AM
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I am a Calc I student having trouble understanding why exactly L'Hopital's rule works and when exactly it can be used. I know this question is general, I just want to gain more of an understanding of the rule...thank you for your time.

Short title. L'Hopital's Rule

6:40 AM
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There is an expression given for a piece-wise linear function, fn(Phi). fn is being a function of Phi: u = u0*cos(w*t-y) = u0*cos(Phi) where Phi = w*t-y Assume u0, w, t are positive Assume u0 > Fy/kf fn(Phi) = Fy + kf * (u - u0) for 0 <= Phi < Theta fn(Phi) = -Fy for Theta <= Phi < pi fn(Phi...

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How to find an integer $x$ such that $140x \equiv 133 \pmod{301}$? There is a hint that $gcd(140,301)=7$

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I have 3 circles: $C_1$ centered at $(0,0)$ with radius 1 $C_2$ centered at $(a,0)$ with radius $a+1$ $C_3$ centered at $(-a,0)$ with radius $a+1$ (so $C_1$ is internaly tangent to both $C_2$ and $C_3$ ) Question: What are the centres of circle $C_4$ and $C_5$ that are tangent to all three ...

Words such as question do not add information to titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (autocomment)Normal Human 22 secs ago
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What is the value of $\lim_{n\to \infty}(\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}...+\frac{1}{2n})$? Please give some hints to proceed .

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for checking it $$lim_{n \to \infty}cos(1/n)=lim_{n \to \infty} \frac{e^{i/n}+e^{-i/n}}{2}=(1+1)/2=1$$ this means that the series diverges is it right thought.

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Actually I want to ask questions about interfaces required for communication between network entities in mobile communication.

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What is the origin and context of the phrase 'solvable in polynomial time' in computer science? Are they related to the notion of 'polynomials' in mathematics?

Title contains problem. Short question. problems solvable in polynomial time
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I am trying to solve a system of ODE's using the backward euler's method in MATLAB. The system has 3 equations with the initial conditions given below. x' = λ - ρx - βxz; y' = βxz - δy; z' = py - cz; x0=43100; y0 = 0, z0 = 0.0033, λ = 388, ρ = 0.009 δ = 0.18, p = 50000, c = 23, β=3.61e-8 Can s...

Question contains please. Tagged matlab. Solve a system of ODE's using backward euler's method
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Let $A=\{\sum _{i=1}^\infty \dfrac{a_i}{5^i}:a_i=0,1,2,3,4\}\subseteq\Bbb R$. Then is $A$ a finite set? the series $\sum _{i=1}^\infty \dfrac{a_i}{5^i}$ always converges to $0$ .So $A=\{0\}$ Is it correct?

Short title. Is $A$ a finite set?

7:24 AM
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Sometimes there may some newbies that post comments as answers. If I flag them as NAA, they will be cleared but the user may never know what they did wrong. On the other hand, if I just leave comments but not flagging them, they can see comments and know what they did wrong. My question is, is t...

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Suppose that X is uniformly distributed on (0,2). A) Find E[X] I got that to equal to 1 B) Find E[e^X] I got that to equal to 3.1946 I am wondering if these are right and if not could you please show me how to do it the correct way.

Short title. Question contains please. Uniformly distributed
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I am trying to compute the expected value of a function V^2, given that V is a normal random variable with mean = 0 and variance = sigma squared?

Short question. [What is E[X] of V^2 given that V is a normal random variable with mean = 0 and standard deviation = sigma](math.stackexchange.com/q/1574848)

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I wanted to use Stack exchange network as a suggestion like here in google https://cloud.google.com/appengine/docs/java/xmpp/?csw=1 How can I achieve this ? Is that any open source API from which I can enable this in my Website? Any help is most welcome.Thanks in advance.

7:44 AM
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Do there exist two dense sub-spaces of a Hilbert space whose intersection is {0}?

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A great friend of mine recently sat for an interview. He was asked a question which has fascinated me since some days now. It is Consider you have 100 balls which look the same but one out of them is either heavier or lighter than the rest . You are given a beam balance , then find out in mi...

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I am trying to find the expected value of the function Z = mV^2/2, in terms of sigma and m, where m is a constant greater than 0.

Short question. [V is modeled as a normal random variable with mean 0 and variance σ 2. What is E[X^2]](math.stackexchange.com/q/1574870)

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I have a question that has been asked twice already (namely, a feature request to be able to link to specific points within a question or answer). The problem is the second was marked as a dupe of the first (even though the first has no good or accepted answer and was fairly poorly worded). It al...

8:02 AM
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Intuitively it seems that function $\sin(1/x)$ should be bounded, but analysis shows it is not the case. The function takes arbitrarily large values around zero. Why it is the case?

Consider replacing (analysis) with a more specific tag for the relevant branch of analysis. (autocomment)Normal Human 50 secs ago
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I have troubles to solve this kind of exercises. For example, let $G_1=<x,y |x^3=y^4=1>$ and $G_2=<x,y |x^6=y^6=(xy)^3=1>$. I want to check that 1) $G_1$ is infinite and nonabelian and 2)$xy^2x \neq 1$ in $G_2$. For the first part, I have seen that it is useful to define a group homomorphism...

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Can we say that $\sum{{a_n}{b_n}}$ converges / converges absolutely?

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What is the total no. of positive integral solutions of: X1 + X2 + ... + Xk-1 < Xkwhere Xi < Xi+1 and each of Xi <= N

Welcome to Math.SE, MD SHAHBAZ SHAFI. This site uses MathJax formatting of formulas. More tips here. (from a bot)Normal Human 1 min ago
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Let $H$ be a non-separable Hilbert space. Assume $E$ is an orthonormal basis in $H$. Let $E_0=\{e_n\}$ be a countable subset of $E$ and let $\{\zeta_n\}$ be a bounded sequence in $H$. Let $E_1$ be a countable susbet of $E$ and denote $p$ by the projection onto $\overline{span\{e: e\in E_1\}}$. ...

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I am working through Parzen and I came across a problem that has completely stumped me. I have an urn which has M black balls and N white balls. Each turn, I randomly reach in and choose one ball without replacement. If the ball is black, I add on white ball to the urn (and no not replace the dra...

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I am considering the following optimization problem: $\underset{u}{\text{minimize }}\quad \underset{v}{\max} f(u,v)$ where for a fixed $u$, the function $f(u, .)$ is piecewise constant. Do you know if there exists any simple approach to solve this kind of problem? Which one should I use? Than...

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$\int e^{x^x}$. taking u = $x^x$ so du= $x^x$[logx +1] dx -> $\frac {du}{[u(log(x) +1)]}$=dx Now to remove log(x) from denominator I took log(u)= x log(x) -> log(x) = $\frac {log(u)}{x}$ Again If I use that log(u) to remove x I get log(x). How to proceed from here, Or is there another me...

8:47 AM
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I have gone through similar questions on meta but as it's still not clear I am asking a different one. Here is a post which is completely off-topic. It's asking about finding an existing Android app and doesn't suit the Stack Overflow (i.e. site for those who code). It is best suited for Android...

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$2^{100} \equiv 1 \ (\text{mod}\ 125)$ and is divisible by $8$. Why then is $2^{100} \equiv 376 \ (\text{mod}\ 1000)$?

8:59 AM
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Like previous year , Winter bash also comes this year with hats. Every hat has a challenge to achieve it.It's really fun to collect hats . But there is no tracking system like tag,badges to track next hat. As Winter bash comes every year, can it be possible to open a tacking system of hats lik...

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Title says it all really, logged in today, got a hat on my profile activity page, a cake to customize my profile picture and a new snowflake icon on the notification bar. So what is winter bash?

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In English, I would generally read the mathematical notation $\bar{A}$ as "a bar" or "big a bar." What would this be in Russian? Thanks.

Questions tend to get more attention when they have a tag for a broad area of mathematics relevant to the question. Some of these tags might fit. (from a bot)Normal Human 1 min ago
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Let $X$ and $Y$ be an independent random variables with exponential distribution $Exp(1)$. Compute $E[\min{\{X,Y\}}|Y^{2}]$. My attempt: I. If we want to compute $E[\min{\{X,Y\}}|Y]$ may be sufficient to use the following formula: $$E[f(X,Y)|Y]=\int\limits_{-\infty}^{+\infty}f(x,Y)f_{X}(x)dx... Short title. [Conditional expectation E[\min{\{X,Y\}}|Y^{2}]](math.stackexchange.com/q/1574928) 0 I want to find the degree of the splitting field for x^3-3x-1 over \Bbb Q and \Bbb F_5. My attempt is contained below. 0 Let X1,X2,X3,... be an i.i.d. sequence of Bernoulli random variables where Xi=0 with probability 0.5 and Xi=1 with probability 0.5. For a fixed value of N, define Xbar = X1+X2+X3+...+XN/N A) Find u(subscript Xbar) = E[Xbar] and Sigma^2(subscript Xbar)= Var[Xbar] This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 47 secs ago 0 How can I find the PDF of the function Z=mV^2/2, in terms of sigma and m, where m is a constant greater than 0? 9:33 AM 0 Let f:V\times V \rightarrow C be a bilinear form in a finite inner product space. Will there always be a single linear transformation T:V\rightarrow V for which f(v,u) = <Tv,u> for each v,u\in V. If not - what's an example of this not happening? (I can prove this for bilinear forms f:V\... Short title. Bilinear form over C 0 I saw this question in triage today. After reading initial lines, It appeared to be spam (Discussing his website with details of its services in a promotive narrative). So I flagged it as spam. After a while, I realized my mistake and flagged it as off-topic because the guy was asking for recomme... -1 I asked this question: How does one read \bar{A} aloud in Russian? How does this decision fit with the majority view here: Questions about how to read mathematical notation If possible, I would like to have the question reopened. Thank you. Edit: I've received a good answer in the comments t... 0 There are several books and articles on topos theory which mention the internal language, but I can't manage to see the big picture from any of them. I would like a soft explanation of how the entities in the definition of an elementary topos come to together and give rise to this internal logic.... Consider adding a tag for a broader subject area to which the question belongs. Some of these tags might fit. (autocomment)Normal Human 20 secs ago 0 Please solve the following integral.$$\int x^2 e^{-\frac{x^2}{2}}dx.$$Short question. Question contains please. Solve the integral \int x^2 e^{-\frac{x^2}{2}}dx 0 Why does 3f_3 + 4f_4 + 5f_5 + ...= 2E? Is there a specific proof for this or is it just due to the fact that each edge makes up parts of 2 different faces. I have looked all over the internet and I cannot find a proof online, everyone just seems to 'assume' that it does. Please help. Thanks Question contains please. Why does 3f_3 + 4f_4 + 5f_5 + ...= 2E 9:53 AM -2 I have a problem with unis 3.1.1 on Virdi AC7000 when transferring users data from terminal to another all user data is transferred very well but without finger print data so I tried to use the UCS SDK_v4.3.4.0 (UCBioBSPCOMLib,UCSAPICOMLib) and when trying to start my app as a server it gives me ... 0 Is it worth migrating this question to MO, from math.SE? It seems elementary but did not get any response on MSE even after 10 days. 10:03 AM 0 Let X be obtained by taking two disjoint copies of the interval [0,2] (with the Euclidean topology) and gluing each t in the first copy with the corresponding t in the second copy, for all t \in [0,2] different from the middle point. Explicitely, one may take the space$$ Y=[0,2]\times...

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How are simplicial complexes more helpful than CW complexes with respect to smooth manifolds? What are some of the benefits of one vs. the other?

Short title. Short question. CW complexes vs simplicial
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Considering statements (1) , (2) , (3) & (4) to be true , $$\sum_{j=1}^B (w_kj + y_kj) + (e_k - b_k)a \leq f_l$$ $$\sum_{j=1}^B (w_kj + y_kj) \leq f_l - (e_k - b_k)a$$ $$\sum_{j=1}^B (w_kj + y_kj) \leq f_l + (b_k - e_k)a$$ Summing up in terms of $k$ , $$\sum_{k=1}^{4}\sum_{j=1}^2 (w_... Short title. jhghjgvgjffgghfghf 10:28 AM 0 Just do it. Swoosh. http://winterbash2015.stackexchange.com/ 0 If x=\pi^{3} and y=3^{\pi} then what is the relation between x and y? I have no idea of how to solve this problem. Please help. Short title. Short question. Question contains please. Relation between two numbers 10:47 AM 0 Looking at sets (in ZF, Set Theory of Kunen) I could not escape from looking at logic as well. A formal language is presented containing basic symbols (\wedge,\neg,\exists,(,),\in,=, and v_{i} for i=0,1,\dots). Also things are said about free variables and bound variables. Formulas are d... 0 I have the following problem. Let H_t be an adapted process with trajectories a.s. of class C^1 on \mathbb{R}_{+}. Compute using simple process \int_o^t H_s d B_s. My idea is to firstly set U_n(s):=\sum_{i=0}^{m(n)-1} H_{t_i^n} \mathbb{1}_{(t_i^n-t_{i+1}^n]} (where of course I consider... 0 I know this comes up all the time but I just want to bring it back one more time. When low rep users edit questions and answers can they please make sure they make they actually contribute to the post with there edits. Today, again, the edit queue is full of one tag edits and, most annoying of ... 0 Custom HTTP method with Nodejs HTTP Server Answer to this question is modifying piece of code in older version of NodeJS, which was working for OP. But with latest version NodeJS files, the accepted answer is no longer relevant. How can I get answers for latest versions? Post new/similar questi... -2 I've done some mistakes on Stack Overflow regarding to post some questions, which may not not be there. They not recieved well questions, so they gave me votedown, e.g. I'm missing something Swapping strings in C [duplicate] How we 5 replaced by 27, since there is no relationship? Is it possib... 0 I have visited http://winterbash2015.stackexchange.com/ to see more about hats It shows me localized description for hats (Russian). A bit strange after English-only SO.com, I'm Ok with English, but thanks anyway But some translations hurt because of typos I did search but couldn't find where ... 0 I know the definition of an outer measure. Let X be a set. An outer measure on X is a function \theta : \mathcal{P}X \to [0,\infty] such that (i) \theta \phi=0 (ii) if  A \subseteq B \subseteq X then \theta A \leq \theta B (iii) for every sequence <A_n>_{n \in \mathbb{N}} of subsets... 11:12 AM 0 I have noticed that since, an hour ago, I asked for my question on how to read a formula aloud to be reopened ( Why is my question on hold? ) some users have begun casting close votes on dozens of old questions on pronunciation. As far as I can tell, there has been no open discussion of this on ... 11:28 AM 0 Can anyone prove the angle theta (smaller angle) between diagonals of a parallelogram is given by the equation cos(\theta)=\frac{a-c}{a+c} where "2*a" is the base length of parallelogram; "2*c" is the horizontal distance to the edge when we draw a vertical line as seen in the picture below. ... 0 Given$$F(x)=\frac{1}{2x}\int_{-x}^xf(t)dt,$$where f:\mathbb{R}\to\mathbb{R} is continuous and f'(0) exists, how can I prove that F'(0) also exists? 0 Let H be a Hilbert space. Some books define an orthonormal basis as one that is in the title. I am using the standard linear algebra definition, that is, an orthonormal basis is one that is a basis and orthonomal in the linear algebra (finite-dim) sense (every element in H is a linear (poss... 11:52 AM 0 Let A=\{\sum_{i=1}^{\infty} \frac{a_i}{5^{i}}:a_i=0,1,2,3 or 4 \} \subset \mathbb{R}. Then which of the following are true: a. A is a finite set. b. A is countably infinite. c. A is uncountable but does not contain an open interval. d. A contains an open interval. Each such seri... 1 I came across this question on meta recently: Make the New Answers to Old Questions real time It got me thinking: why can't newer users see new answers to old questions alerts (10000 rep required)? As Stack Overflow becomes full of good general questions, I think the scope for good non-duplicat... 0 I created a custom tab, consisting of the following tags: windows-phone-8 windows-10 windows-10-mobile windows-universal win-universal-app all combined with any. However if I open up the tab, I just see the message "That's a miss" Strangely if i set the cursor in the edit field and move it to... 0 Let triangle \triangle{ABC} have incenter I. Prove that the Euler lines of \triangle{AIB}, \triangle{BIC}, \triangle{CIA}, \triangle{ABC} are concurrent. 0 The theorem is: Let X be a set and \theta an outer measure on X. Set \sum= \{E: E \subseteq X, \theta A=\theta(A \cap E)+ \theta(A \backslash\ E) for every A \subseteq X\} What is the intuition behind this definition? and what does the Caratheodory method try to achieve? 12:22 PM 0 I've got what I think is a proof, am wondering if I've made a mistake. Proof by contradiction: Suppose sqrt(n)=a/b, with a and b being integers and coprime meaning a/b is rational. Square it, so n=a^2/b^2 and take the b^2 over: b^2 n = a^2 The way I see it, since a^2 is taking the prime factor... This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 21 secs ago 0 When you have <= 5 votes left in a day, there's a mini-dialog that pops up informing you of this fact. There's a button on the end of it that lets you close it early, before it automatically closes. This button is usually centered vertically in the box, but today it's broken: The same is appar... 0 I am looking at the following: Could you explain to me what a constant field is? Short title. Short question. What is a constant field? 0 According to the help page on privileges. In particular Established user. The user receives the ability to see expandable user cards on other users. This appears when the user reaches 1000 reputation. However I am only at just over 700 and I am able to see them. Is this a bug or something that w... 0 enter image description here How to integrate (cos x)^n.(sin x)^m with reduction formula. the actual steps please in terms of (n-2,m) and in terms of (n, m-2) like in the image shown I'm stuck halfway Thanks https://en.wikipedia.org/wiki/Integration_by_reduction_formulae 0 Find the value of the series \sum_{i=1}^ \infty \dfrac{n}{2^n} The series on expanding is coming as \dfrac{1}{2}+\dfrac{2}{2^2}+.. I tried using the form of (1+x)^n=1+nx+\dfrac{n(n-1)}{2}x^2+.. and then differentiating it but still it is not coming .What shall I do with this? Tall formulas in titles break the layout of question lists. Please replace \dfrac with \frac in the title. (autocomment)Normal Human 21 secs ago 0 I cannot seem to solve what I think should be a straightforward intersection theory question in Ravi Vakil's algebraic geometry notes. Let X be a scheme and Y a closed subscheme of dimension less than or equal to n, and \mathscr{L}_1,\ldots,\mathscr{L}_n be a collection of line bundles o... 0 I really need help on this question. diagram: http://media.apexlearning.com/Images/200702/13/1ef91461-c2f5-4d1a-9188-5c5fe1fd849a.gif 1 The question reads : A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares of length h from the corners and folding up the sides as in the figure below: Suppose that the box height is h = 3 in. and that it is constructed using 134 in.^2 of c... Words such as question do not add information to titles. Please edit the title so that it better describes the specifics of your question. Do not hesitate to make it longer or include a formula if needed. More tips here. (from a bot)Normal Human 20 secs ago 0 Show that there is no perfect square whose last three digits are 341. Solution: Let x be any integer. Note that if x^2 ended with the digits 341, then we would have$$x^2 = 1000k+341$$for some integer k, so$$x^2 = 1000k + 341 = 341 = 5 (mod 8)$$. We make a table of squares modulo 8.$$ x: ...

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An equation of motion when a particle moves in a resting medium is given by dv/dt=-(kV+bt) where k and b are constants.Given that v=u,when t=0..show that v=b/k^2-bt/k+(u-b/k^2)e^-kt

Welcome to Math.SE, Simon Kupalia. This site uses MathJax formatting of formulas. More tips here. (from a bot)Normal Human 21 secs ago

1:05 PM
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I have a professor who made a very good point about the data titanic analysis during a lecture this week. I am still however trying to better understand. He argued that it is also possible to have a model of titanic data (GLM) using Poisson rather than the typical Binomial approach. I am curious ...

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So, first of all I'm gonna start with stating that I'm a complete noob in mathematics that started doing this as a hobby. I encounter problems that I can't figure out on a regular basis, like a few times per page but I usually find someone to help me. This time those same people were of no help s...

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I have just started revising number theory and I am getting stuck on a lot of the "prove that" questions. Any tips and advice would be much appreciated!

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I am in calculus class right now and I have no idea. I'm sorry for my ignorance.

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По правилам русского языка — «надеть шляпу»

1:24 PM
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I'm totally stuck at this problem and any help would be appreciated: Suppose $R_\rho \in M_2$ denotes a reflection across a line which is through the origin and at a anticlockwise angle of $\rho$ with the x-axis. The question asks that for any $n \in \mathbb{N}$, does there exist a subgroup of $M... 0 Over 2,300 years ago Euclid proved that the number of primes is infinite, so two possible questions come to mind: How many primes are there less than the number x? There are infinitely many primes, but how big of an infinity? This document will focus on the first question. The seco... 0 If h(t) represents the height of an object above ground level at time t and h(t) is given by h(t)=-16t^2+13t+1 find the height of the object at the time when the speed is zero. Suppose h(t)=t^2+14t+7 . Find the instantaneous rate of change of h(t) with respect to t at t=2 . Suppose G(x)=6x^2+x+... This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 21 secs ago 0 Hi can anyone help me on this problem? In have the function 2^n*(2n+1)-1 and I need to prove that the function has an inverse function. So I did: f(x,y)= 2^n*(2n+1)-1 f(x,y)=t, where t=59 so: 2^n*(2n+1)-1 =59 2^n*(2n+1)=60 (Factorize 60 it becomes) 2^n*(2n+1)=2*2*3*5 after that I am los... This site uses MathJax formatting of formulas. More tips here. (autocomment)Normal Human 21 secs ago 0 $$x''=-2\beta x'-x+\gamma\cos(\omega t)$$ with$\beta,\gamma,\omega$positive constants. I started by finding the homogeneous part of the solution by solving$x''+2\beta x'+x=0$and found $$x_{hom}=c_1e^{\lambda_+ t}+c_2e^{\lambda_- t}$$ with$\lambda_{\pm}=-\beta\pm\sqrt{\beta^2-1}$. Now to find... 0 The problem statement is: Let D be the domain consisting of all points satisfying Im$z>0$and (Re$z)^2$+(Im$z−1)^2>1$. Map$D$onto the upper half plane. So the domain is everything on in the upper half plane, minus the circle of radius 1, centered at$(0,i)$. I first applied the logarit... 0 Let$G$be an abstract group (say, finitely generated). Endow$G$with the profinite topology. I would like to get comfortable with computing the closure of subgroups of$G$. More specifically, I would like to understand how to use the profinite completion of$G$to do that. If$G$is residual... Welcome to Math.SE, Nils. Consider adding a tag for a broader subject area to which the question belongs. Some of these tags might fit. (from a bot)Normal Human 21 secs ago Title contains problem. Tagged proof-verification. Compound Interest : Clarification Of The Given Solution To This Problem. 0 I am not relieved of the following problem and trip. Let$\varepsilon>0$be a small parameter,$a>0$be a given constant,$x_{\varepsilon}\in(0,a)$be a given sequence such that$x_{\varepsilon}\to a$as$\varepsilon\to0$and$f:[0,a)\times[0,a)\to\mathbb{R}$be a continuous function such that$...

1:43 PM
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We've noticed this new feature in the Ruby chat room this morning: http://chat.stackoverflow.com/transcript/message/27523117#27523117 If you check our room's transcript, you'll see that a couple minutes before I deleted a message, which contained the same code from the gist. When sample code ...

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In an exam there are 10 questions. If you answer correctly to a question, you get $1$ point. If you answer incorrectly to a question, you get $-1$ point, or lose a point. If you don't answer to a question, you get $0$ point. You pass the exam if you get at least $7$ points. A pupil read the ques...

Welcome to Math.SE, curious. Tag (contest-math) should not be the only tag a question has. Please add a tag for a subject area to which the question belongs. (autocomment)Normal Human 21 secs ago
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Show that the number of ways to stack coins with n coins in the bottom row is denoted by Catalan number Dn = (2nCn)/n+1. I have tried in the way described in the picture below

Title contains problem. Short question. A problem concerning catalan number
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Found this on a textbook and I know I am missing out something really simple as it's been a while for me with vectors so here it goes:If $\Bbb P=mi-2j+2k$ (where i,j,k are unit vectors) and $\Bbb q=2i-nj+k$ are parallel to each other, then find $m$ and $n$

Short title. Parallel Vectors

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