@TedShifrin I was looking at a few maximization problems. I can solve them with Lagrange maximization just fine, but I confused myself a bit trying to do it the plain vanilla way. E.g., minimize $x + y + z$ with constraint $xy^2 z^3 = 180$, $x, y, z$ positive. The function I have to minimize is $F(y, z) = y + z + 180/(y^2z^3)$. Differentiating tells $(2, 3)$ is the only crit pt. Second derivative test tells it's a local minima.
But what I am having trouble with is for proving this is a global one. I realize I need to construct a compact $X$ containing $(2, 3)$ such that $F$ is more than $F(2, 3) = 6$ outside the interior of $X$. But I can't seem to construct $X$. I guess it should be bounded below by $y^2z^3 = 1$. Is there a general procedure for doing this?
No general procedure. You just need to cook up the compact set so as to guarantee that the function is strictly less than $F(2,3)$ everywhere on the boundary and outside.
Excuse me, is there an example which explains why Lebegue integral does integrate over range? It is usually said to contrast with Rieman after lots of definitions about countable sets and measures where I am completely lost and just saying that we integrate over y axis does not explain me anything. I want to see WHY. How are all these definitions bring me to integration over values.
i need help, i have that $\lambda_n\rightarrow +\infty$ and $(y_n)\subset \mathbb{R}, y_n\rightarrow+\infty$ Is $$ [B_{\lambda_n R}(0)\setminus \overline{B_{\lambda_n r}(0)}]\setminus B_{\frac{\lambda_n r}{2}}(y_n)=B_{\frac{\lambda_n r}{2}}(y_n)$$ ?
Hi. Why is 8 not a prime element in ring of integers? 8|2*8 \implies 8|2 or 8|8, which is true...
Def: An element p of a commutative ring R is said to be prime if it is not zero or a unit and whenever p divides ab for some a and b in R, then p divides a or p divides b.
There is an exercise in my textbook.
Suppose ‘$m$’ denotes Myfanwy, ‘$n$’ denotes Ninian, ‘$o$’ denotes Olwen, ‘$Fx$’ means x is a philosopher, ‘$Gx$’ means x speaks Welsh, ‘$Lxy$’ means $x$ loves $y$, and ‘$Rxyz$’ means that $x$ is a child of $y$ and $z$. Take the domain of discourse to consist...
