I'm having some trouble with this question. I don't really understand what it is asking. $\theta$ and $\alpha$ are acute angles in standard posi...

I'm studying for an exam and I'm not sure how to do this. I understand what the definitions mean (for the most part) but I'm not sure how t...

Find all points $(x,y)$ on the graph of $y=\frac{x}{x-3}$ with tangent lines perpendicular to the line $y=3x-1.$ My thoughts on this problem: First I shou...

I am trying to convince my friend that the integral of $0$ is $C$, where $C$ is an arbitrary constant. He can't seem to grasp this concept. Can you g...

Given $\sum a_n$ and $\sum b_n$ we define the Cauchy product to be $\sum_{k = 0}^{n}a_kb_{n-k}$. I need to prove that if both $\sum a_n$ and $\sum b_n$ ar...

I am not sure I understand the difference between free modules and finitely generated modules. I know that a free module is a module with a basis, and tha...

If i have this: $a + p = 3$, what means express in terms of $a$? , I know that this is elementary, and although I know how to do more difficult things, I ...

I am looking for a closed form expression for the following integral. One approach that comes to my mind was to use Laplace transform, using the following...

$$\sin(a+b) = \sin(a) \cos(b) + \cos(a) \sin(b)$$ How can I prove this statement?

I have never seen a definition of functoriality, but this word keeps coming out in texts on category theory. Wikipedia redirects to the page about functor...