The real number x when added to its inverse gives the min mum value of the sum at x equal to 1) 2 2) -2 3)1 4)-1

Given that on 31.XII.2000 closing price of company's share was $50\$$ . Assuming that a company during next ten years will give $5\$$ of dividend at the end of each year. What is the lowest price to sell a share after 10 years that would guarantee minimum of 10% rate of return? I think it is a q...

everyone I have troubles completing this exercise. The exercise My solution But my math professor says my solution is wrong. Could anyone tell me where I am missing his logic?

We define Indefinite integral of a function $f$ as $\int f(x)dx$ which is the collection of anti derivatives of the function $f.$ But in many books it is written that for an integrable function $f$on $[a,b],$ $\int_{a}^{x}f(x)dx$ is the indefinite integral of $f.$ What is the difference between...

I'm writing a paper on the Mandelbrot set and want to add some examples of iteration to it to show values that are members of the set and to show values that are not members of the set. What's the cleanest way of doing this?

I have this topological space $(\mathbb{R}^2,\tau)$ where the basis of $\tau$ is $\sigma=\{\Omega_r, r\in \mathbb{R}_+\}$ where $\Omega_r=\{(x,y)\in\mathbb{R}^2, x=r \cos(t),y=\sin(t); t\in[0,2\pi[\}$ let $A=\{(x,y)\in\mathbb{R}^2, |x+y|>2\}$ How to find $\overline{A}$ and $\overset{\circ}{A}$ ...

I need help with this exercise: Let X be a complex Banach space. A bilinear functional on $X\times X$ is a map $B: X \times X\rightarrow \mathbb{C}$ such that for all $x,y \in X$, the maps $B(x,\cdot),B(\cdot,y): X \rightarrow \mathbb{C}$ are both linear. Consider the product space $X\ti...

Suppose I have two complex bivariate homolorphic functions $f(z,w)$ and $g(z,w$) such that $$ \frac{\partial f}{\partial z} = \frac{\partial g}{\partial w} $$ $$ \frac{\partial f}{\partial w} = - \frac{\partial g}{\partial z} $$ That is, the two functions behave as a "super-holomorphic" functio...

I have a Matlab code that requires plotting of an Ellipse from a Matrix. I know this can be done by taking SVD(singular value decomposition) of the Matrix, but I need to know how? I couldn't find any tutorial online which can do this.

Let $V = C^0([a,b])$ be the vector space of continuous functions $f: [a,b] \rightarrow \mathbb{R}$. Prove that $S=\lbrace f(x) \in C^0 [a,b] \vert \int_{a}^{b} f(x) dx=0\rbrace$ is a subspace of $V$. What I tried: I thought of using the fundamental theorem of calculus to get f(b) = 0 and then...

$\forall F \in H^* \exists! y \in H \mbox{ such that } F(x)= \left \langle x,y \right \rangle $ Suppose $F \neq 0$. Let be $$M=KerF.$$ M is a closed vector space. Let be $h \in M^{\bot}$ with $\left \| h \right \|=1$. So $F(h)=1$, and consider $F(h)x-F(x)h$. This element is in $M$ because $F...

If: https://en.wikipedia.org/wiki/Daniel_Tammet is such a great mind in mathematics, what did he solved from the following list?: https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics

The identity I had trouble to prove was $(n-1Cr-1)(nCr+1)(n+1Cr)=(nCr-1)(n-1Cr)(nCr+1)$ If someone can edit and write the Choose correctly I'd be glad

How many ways to arrange $2p$ kids ($p$ boys and $p$ girls) in circles, such that there are at least 4 kids in any circle (no order between circles, but there is order inside), between each $2$ boys there is $1$ girl, and between each $2$ girls there is $1$ boy, and every kid is chosen...

How do I solve this equation, what are the steps that I should do? Use separation of variables to solve Laplace’s equation $$\frac{\partial ^2u}{\partial x^2}+\frac{\partial ^2u}{\partial y^2}=0 , \:\:\:\:\:\:\:\:\:\:\:\:\: 0<x<2, \:\:\:\:\:\:\:\:\:\:\:\:\:\:\: 0<y<1$$ Assume the following bou...

If f is a group homomorphism from group (G,*) onto a group (H,+) and e is the identity in G, then prove kernel of f={e} if and only if f is an isomorphism. Help!!!

Let $X$ be a finite inner product space and $A:X\rightarrow X$ a linear transformation. If $A$ is self-adijoint and if $A^{2}x=0$ then $Ax=0$.

Here x is a complex number. A little help would be appreciated.

What is the fastest way that you can do by hand? For example: (just a simple example, the answer should be general of course) $x^4 -4x^3 +8x$ or $2x^2+3x+1$

How can we compress the following matrix into CSR row format? 0 0 0 0 4 3 0 0 0 I think it should be like this: rowStartIndex = {0,0,0,2} columnIndex = {1,2} values = {4,3} But when i try to make SPMV (sparse matrix vector multiplication) i get the wrong result according to the followin...

Let $W = \lbrace A \in M_n(\mathbb{R}) | Tr(A) = 0\rbrace$ where $Tr(A)$ is the trace of A (i.e. equal to sum of diagonal elements of A). Show that $W$ is a subspace of $M_n(\mathbb{R})$. What I tried I tried to construct a matrix $M_3$ e.g. \begin{array}{cccc|c} 1 & 0 & 5 &\\ 0 & -4 & 1&\\ 0 &...

Suppose that for all z ∈ D and all n ∈ N we have that fn is holomorphic in D and |fn(z)| < 1. Also suppose that limn→∞ (Imfn(x) = 0) for all x ∈ (−1, 0). Then lim (n→∞ Imfn(1/2) = 0).

Depict the corresponding hypercube with the question mark enter image description here

Can we assume that c=1 is not a member of the Mandelbrot set after only 2 iterations when $x_2 = 2$ or do we need an iteration to be above 2.0 and not equal to it?

My ODE is: y''=W/H I was told that I could use the method undetermined coefficients to solve this but I got stuck. I was thinking I could take the integral of it twice with respect to x? I know the homogenous equation is yh=C1+ xC2 but after that I am stuck. If I can use any other method that w...

we have two lines: L1: x=1+t1, y=t1, z=2-5t1 L2: x=-1+t2, y=2+t2, z=1-t2 where t1 and t2 are scalars. L1 crosses the xz-plane in point P and L2 crosses the yz-plane in point Q. the question then continues to ask for plane and line equation.... My question is that someone started to answer thi...

Let $x_n$ be a sequence that converges to $a$. ($a$ final limit) prove that if $\lim_\limits{n\to \infty}\frac{a_{n+1}}{a_n}=L$, then $|L| \le 1$ any suggestions guys? I thought about proving by contradiction by suggesting that $L>1$ then by the convergence test it would mean that $a_n$ diverg...

Problem: Given a graph G (as an adjacency matrix or a grape graph object), and a permutation $\pi \in S_n$. Find an isomorphic graph $G'$ under $\pi$ as another adjacency matrix. The concept is fairly straightforward, but repeated need for such a result requires an algorithm to do a quick analys...

Let V=<{cosx;sinx;cos^2x;sin^2x}> and W be the vector space of all continuous function.the derivative d is a linear map. For d :V-->W find a basis for the null space and the rank of d, and a basis for the range of d.

I want to take the inverse laplace transform of $$\frac{e^{-s}}{s(s^{2}+1)}$$ So I separate the equation into $$e^{-s}\times\frac{1}{s(s^{2}+1)}$$ Now, I take the partial fraction of $\frac{1}{s(s^{2}+1)}$. I get $$\frac{A}{s} +\frac{Bs+C}{s^{2}+1}$$ $$\frac{A(s^{2}+1)+(Bs+C)s}{s(s^{2}+1)}$$ ...

I need help with the following: y´ = Ay^2 + By + C How do I solve? Also I must apply the method to find v(t) for free fall with air resistance equation.

The Face of the problem I have worked with the range of inverse sin which didn't give me anything

I am stuck along the way while trying to prove that there exists a nonzero functional $f$ on $V$ such that $T^tf=cf$ for any scalar $c$ and a nonzero $\alpha\in V$ s.t. $T(\alpha)=c\alpha$. Where $V$ is a finite dimensional vector space over the field $F$ and $T$ is a linear operator on $V$. Her...

I've been searching for an hour to find why convergence in Lp doesn't imply almost sure convergence. Can somebody explain why?

Let's say A=(0,0,0) , distance d from A to B and orientation angle from B to A is given(in degree) (x1,y1,z1) with reference to A. How will I find coordinates of B.

I'm currently learning about generalized eigenvectors, and I'm not sure if I'm thinking about this problem correctly. If I'm given a square matrix $A$ that has a generalized eigenvector of order k>1, the direction of this eigenvector $\vec{v}_k$ is uniquely determined. I think this is true, sin...

(This is problem P-3.7 from the book 'Signal processing first') Let $x(t) = 2\cos(\omega_1)\cos(\omega_2) = \cos(\omega_1 + \omega2)+\cos(\omega_2 - \omega_1)$ Then what relation needs to hold for $\omega_1 + \omega2, \ \omega_2 - \omega1 ,\ \omega_1$ and $\omega_2$ such that $x(t)$ is periodic...

could anyone clarify the difference between the ritz value and harmonic ritz value? Is the minimal eigenvalue the harmonic one ?

Could someone explain to me the splitting field please. I am having some trouble figuring out how it helps with polynomials. Given f(x)=$x^4+2$ in $ Z_7$ determine its splitting field. I would appreciate the help on this concept.

Let k be positive integers $\lim_{x\rightarrow \infty }\dfrac {2} {x}\sum _{k\rightarrow 1}^{x}\ln \left( \dfrac {x+k} {x}\right)$

Consider the following vectors in R 3 V1 = 1 √ 3(1,1,-1), V2= 1 √ 2(1,-1,0), V3 = 1 √ 6(1,1,2) a) Show that they form a basis of R 3 . (hint: compute the inner products v t i · vj). b) Work out the coordinates of a vector x = (x1,x2,x3)in the basis {v1 , . . . , v3}, that is the numbers c1, ...

I want to show that $u(x)=\int_0^1 \frac{tdt}{|x-te_1|}$ is harmonic on $\mathbb R^3\setminus\{te_1:t\in[0,1]\}$ where $e_1=(1,0,0)^T$. So far I've computed the integral: $u(x)=sign(x_1-t)(x_1log|x_1|-x_1log|1-x_1|-1)$ However I don't seem to get the Laplacian right since ${u_x}_x=\frac{1}{(...

I'm trying to do CRT with the factorization of 63 as $3^2$ and $7$, however in my solution I'm provided, I am unable to figure out why some steps were taken. I get the GCD linear combination $(9,7)$ is $1 = 4*7 - 3*9$, but why is the inversion of the reduction map $-27x + 28y$ rather than $28x -...

What do with it? I try to resolve through L'Hopital, but it's so difficult for first course. $$\lim_{x\rightarrow\pi}\frac{\cos(\frac{x}{2})}{e^{\sin(2x)}-1}$$ Thanks

Is there a program that can simplify algebraic expressions with the TI-83 calculator?

$x^{n+1} = Mx^{n} + f$ is fixed-point iteration for solving the equation $x = Mx + f$, i.e., $(I-M)x = f$. The error $e^{n} = x - x^{n}$ How does one get $e^{n}=M^{n}e^{0}$?

In studying eigenvectors, I have stumbled across the following matrix :$$\begin{bmatrix} 0 & 1\\ 0 & 0\\ \end{bmatrix}$$ If I were to find the general solution for this matrix, how would I approach it? Would 1 still be a leading entry since its column is 0? Would it be a free-variable? The answ...

A and B toss a pair of coins alternatively. One who gets two heads together will win the game. If A starts the game, find probability of B winning the game. Can anyone guide me how to approach this problem?

Let $ A =({ x\in R^3 : |x_1| + 2|x_2| +|x_3|^3 =1 })$, and let $ p \in R^3-A $ Then, show that there exists a point $ y \in A $ that is closest to p among all points in A, noted that R^3 has the Euclidean metric. The question seems really challenging.I am thinking of how to find such y in A so ...

What is the cardinality of all cardinalities ? It seems to be uncountable. But Can it determined exactly ?

We consider the differential equation $Ly=f$ in the ring of exponential sums $\mathbb{C}[e^{\lambda x} \mid \lambda \in \mathbb{C}]$ so we have that $f=\sum_{i=0}^n C_i e^{\lambda_i x}$. If we apply the superposition principle we have to solve differential equations of the form $Ly=e^{bx}$/. ...

Could someone show me how to multiply in say $S_4$. I know how to multiply say $(4321)(2341)$ but when it comes to ones that do not contain $4$ terms, like $(34)(231)$, I have no idea how to handle this. We do from left to right.

Operation + is defined by the following formula: (a, b) + (c, d) = (a + c, b + d). Operation ∗ is defined by: (a, b) = (ac + bd, ad + bc).

I am trying to understand what a non-crossing partition means. I was reading a paper and it states A partition is noncrossing if there do not exist four distinct elements $$a < b < c < d$$ with $a, c$ both in one block and $b, d$ both in another. This doesn't make any sense to me, So I mean I wa...

Consider the PDE problem for the wave eq. $$\begin{align} u_{tt}-u_{xx}+2u & = 0, & 0<x<1, t \in \mathbb{R} \\ u_x(0,t) = 0,u_x(1,t) & = 0, & t>0 \\ u(x,0) = 0, u_t(x,0) & =\cos(2 \pi x), & 0<x<1 \end{align}$$ Define the energy solution $u(x,t)$ by $$ E(t) = \frac{1}{2} \int_0^1 ((u(x,t))^2+(u_...

Matrix $A \in \mathbb{C}^{2015,2015}$ satify condition $A = A^{2}$. Show that: $ \mathbb{C}^{2015} = {ker} A \oplus {im} A $

I'm a 19 year old, who will be 20 in may. I didn't go to the greatest high school, and I didn't get the proper education to prepare me for college. I need to make a study plan for myself to truly learn and understand what I will need to complete a degree in Computer Science. My studies will st...

I have a question regarding transformation matrices. I have two images both showing a table. I have coordinates of the corners of the tables, and now I want to apply a transform to 1 of the images so that the tables are equally shaped, rotated and translated. Long story short, I want to know if I...

Dear mathematicians in MSE: Although I am only a math learner on undergraduate level (assuming I had only finished one-year undergraduate analysis and linear and abstract algebra), I am really interested in understanding the seven millennium problems. Trying to understand this kind of open probl...

$$\int_0^{10}\int_x^{10}\frac{x}{1+y^3}dydx$$ I assume there's a neat substitution but I can't see one. Using fubini's theorem doesn't seem to be much help either. Thanks!

I would like a verification of a proof of the following statement. Let $f : \mathbb{R}^p \to \mathbb{R}^q$ be a continuous function. Show that if $A$ is a bounded subset of $\mathbb{R}^p$, then $\overline{f(A)} = f(\overline{A})$. Let $x \in \overline{A}$. Then there exists a sequence $\{x_n\}$ ...

Surface f(x,y)=x^2+4y^2-x+2y on the region bounded by x^2+4y^2=1. Finding the critical points of the surface within the region was easy enough, I found a minimum at (1/2,-1/4). What I'm having trouble with is finding the critical points along the boundary. I can plug in the equation for the regi...

I need help with this Fourier transform computation. $$F(w)=\int_{-\infty}^{\infty} e^{-|x|+ix}e^{-iwx} \, dx$$ Need help to compute.

I'm havin trouble isolate this variable: $$x^2\sqrt{3}+x(\sqrt{1-x^2}-1)-\frac{\sqrt{3}}{2}=0$$ Can someone help me? :p

Can someone walk me through how to find dy/dx (one of the problems I'm reviewing in my Calculus book): $$\int_{1/x}^{2} t \sqrt(t-4), dt $$ I know I need my (x) value to be in the numerator so I can flip it and put a negative sign in front: $$-\int_{2}^{1/x} t \sqrt(t-4), dt $$ Which is equiv...

How can I show T is compact when T is defined as $$ \text{T :}\,\ell^2 \to\ell^2\,\text{by Tx=y where} \,y_j=\alpha_jx_j\text{and}\,\alpha_j\to0\,\text{as}\,n\to\infty$$

The speeds of cars (in km/h) as they travel down the 406 are measured with a radar gun. Suppose 15 speeds are recorded, with the following summary statistics: minimum=89, maximum=121, ∑𝑥=1557 and ∑𝑥^2=162991. I know how to calculate variance when given a set of values, the problem I'm having ...

I'm studying for my final and I seem to forgot how to do some of these questions. Could I get some help. A dot.com company ships products from three different warehouses in Boston, and Chicago, and Seattle. Based on customer complaints, it appears that 3% of the shipments coming from Boston are ...

I'm working on a problem in probability and got to the sum $\sum_{k=0}^{{n-1}}\frac1{1-\frac kn}$. I tried changing its form to $\sum_{k=0}^\infty\frac1{1-\frac kn}-\sum_{k=n}^\infty\frac1{1-\frac kn}$ but didn't get anywhere. Any hint?

I would like a help calculating the Inverse Fourier Transform of Absolute cos[(2 pi f)/100]

the question is: 1.Pick an appropriate branch of the function $$ f(z)= log(iz) $$ 2.find $$\frac {dw}{dz}$$. 3.state where the formula $\frac {dw}{dz}$ is valid?

Hello guys I have spent hours trying to solve this but I get stuck. I couldnt find help in the book or anywhere else. Thank you. if tan(t)=-1/2 is in Quadrant II find sin(t)+cos(t)

Please consider the following website: http://www.kean.edu/~fosborne/bstat/06evar.html In this website, they calculate s to be about $0.391868$ but in the calculations they use $0.391868$ for the value of $s^2$. Therefore, I feel they are wrong but I am not sure. Therefore, I am hoping somebo...