I "created" this excercise on my own when I worked on a task relating to stochastics, but I might need a little bit of help. Task Let $M = \{1, 2, ..., N\...

I have this homework question I am working on: The base of a sand pile covers the region in the xy-plane that is bounded by the parabola $x^2 +y = 6$ and ...

Let's say we have a line $L$ with positive slope that intersects $(0,0)$ and makes an angle of $\theta<90^\circ$ with the $x$-axis ("on top" of th...

How to solve the following indefinite integral $$\int \tan^{3}x \sec^{3/2}x \; dx$$ to get the solution in the form of $$\large\frac{2}{7}\sec^{7/2}x - \f...

I am looking at the following exercise: Describe four different geodesics on the hyperboloid of one sheet $$x^2+y^2-z^2=1$$ passing through the point $(1,...

The proof is from the book Advanced Calculus: An Introduction to Linear Analysis by Leonard F. Richardson Theorem (Bolzano-Weierstrass): Let $x_n$ be any ...

I've been going through Munkres' Topology on my own, and I've come across an exercise where I can't even understand the question. It i...

I have a differential equation $$xy''(x) +(n+1-x)y'(x) + ay(x)=0.$$ If I set $x=r^t$ then how to plug in this and how to use change of vari...

I have been given two points $P(0,1,3)$ & $Q(-1,5,2)$, both of them crosses a line in space. The third point is supposed to cross the line, but there ...

I am mimicking the argument of Hatcher here from example $0.15$ of page no. 15. What the author says is as follows $:$ To verify the homotopy extension pr...