I'm working on a graphing web tool using JSXGraph, The user should be able to draw different functions. I was able to allow the user to draw quadrati...

Calculate $\int{ \frac{e^z}{z^2(z^2+3)}}dz$ over the rectangle $x=2,x=-2 ,y=2,y=-2$. What i did is find the roots of $z^2+3$ break the $\frac{1}{z^2+3}$ i...

When I was first introduced to the idea of an asymptote, I was taught about horizontal asymptotes (of form $y=a$) and vertical ones ( of form $x=b$). I wa...

For any linear transformation $T:\mathbb{Q}^{4} \to \mathbb{Q}^{4} $, does there always exist a non-zero T- invariant subspace? As we know For any linear ...

Can someone confirm if my prove is right? Theorem. The product of two consecutive integers is always even. Proof. Define a number $n$ such that $n:=2k$ wh...

Suppose we flip a coin until we see a head. What is the expected value of the number of flips we will take? I am pretty new to expected value, so I tried ...

I'm interested in the potential of such a technique. I got the idea from Moron's answer to this question, which uses the technique of differenti...

I'm teaching my self topology with the aid of a book. I'm trying to prove the following is a topology: Let X be an infinite set. Show that $\mat...

Let $A = \{0,1,2,3,4\}$ and define a relation $R$ on $A$ as follows: $$R = \{(0,0),(0,4),(1,1),(1,3),(2,2),(3,1),(3,3),(4,0),(4,4)\}.$$ Find the distinct ...

Consider the differential equation $x'=x^2-9$ a. find the stability type of each fixed point To find the fixed points, I set this equal to $0$, right...