## Line integral under surface defined by meshgrid values – Python

I need to calculate the line integral between two points (x1,y1) and (x2,y2) under a surface defined by values on a meshgrid. I’m not exactly sure on the best tool/approach to use for this process …

## The maximum volume of a box

Trying to write a simple web app to solve the following common calculus problem in JavaScript. Suppose you wanted to make an open-topped box out of a flat piece of cardboard that is L long by W wide …

## \$lim_{xrightarrowinfty} e^{-x^2}e^{2x}\$ (epsilon-delta proof)?

I am struggling to develop an epsilon-delta proof for the following: \$lim_{xrightarrowinfty} e^{-x^2} e^{2x} = L\$ (unknown, believed to be 0) I am aware that to do so, we must show \$existsbeta …

## How to sketch image under function on given set

For the function, \$f(r,theta)= (rcostheta , rsintheta )\$, I want to sketch the image under \$f\$ of the set \$S=[1,2]\$ x\$ [0,pi]\$ My first step was to find the images of \$f\$ along the borders of …

## Schwarz inequality for multiple integrals: \$left[int_A f(x)g(x) dxright]^2 le int_A f(x)^2 dx cdot int_A g(x)^2 dx\$

If \$f,g:Ato mathbb{R}\$ are integrable, prove the Schwarz inequality \$\$left[int_A f(x)g(x) dxright]^2 le int_A f(x)^2 dx cdot int_A g(x)^2 dx\$\$ This is that type of question that …

## Prove that \$underline{int_A}{f(x) dx} + underline{int_A}{g(x) dx} le underline{int_A}{[f(x) + g(x)] dx}\$

Question: Let \$f,g:Atomathbb{R}\$ bounded in the set \$A\$. Prove that a) \$\$underline{int_A}{f(x) dx} + underline{int_A}{g(x) dx} le underline{int_A}{[f(x) + g(x)] dx}\le …

## \$P_3(x)\$ and \$R_3(x)\$ of \$f(x)=e^{-3x}+3 sin (x)-1\$

the maclarin series for \$sin(x)\$ is \$\$ sin(x)=sum^{infty}_{k=0} frac{(-1)^k*x^{2k+1}}{(2k+1)!}\$\$ so summation to \$k=3\$ \$\$ begin{aligned} sum^{k=3}_{k=0} frac{(-1)^k*x^{2k+1}}{(2k+1)!} &…

## Uniform contiunuity of \$f\$?

If \$g \$ is uniformly continuous and \$g(x) = (f(x))^2\$,\$f(x) geq 0\$, then is \$f\$ uniformly continuous? So, \$forall epsilon > 0 , \$ there exists \$delta > 0\$ such that \$forall x,y in Bbb{R}\$…

## difference between \$+infty\$ and \$infty\$

I’m taking Mathematical Analysis “I” and I’m studying limits where I have limits to the infinity, but I don’t know what’s the difference between \$lim_{x to infty}\$ and \$lim_{x to +infty}\$ I …

## \$lim_{xto 0}frac{sin(x)-x+frac{x^3}{3!}-frac{x^5}{5!}}{m x^n}=frac{8}{7!}\$

If \$\$lim_{xto 0}dfrac{sin(x)-x+dfrac{x^3}{3!}-dfrac{x^5}{5!}}{m x^n}=dfrac{8}{7!}\$\$ then find \$m+n\$: My attempts: note that \$\$sin(x) = x – frac{x^3}{3!} + frac{x^5}{5!} – frac{x^…