I started the problem but I am confused how to set up. f(x) = 5cos(x) f(11pi) = -5 f'(x) = -5sin(x) f'(11pi) = 0 f''(x) = -5cos(x) f&#...

If we have topological space $\mathbb{R}$ equipped with the co finite topology. If we have finite subsets in consideration they are definitely closed beca...

I am looking for a polyhedron which consists only out of 15 quadrilateral faces? Does such a thing exist?

What point on the line $y=2x+4$ is closest to the origin in $\mathbb{R}^2$? What is the distance from this point to the origin? I know the point closest t...

$A$ is an $m\times n$ matrix and $B$ is an $n\times m$ matrix. $$ \det(I_m + AB) = \det(I_n + BA) $$ Solution: I found this guys: $$ \det\begin{pmatrix}I&...

This is probably a silly one, I've read in Wikipedia about power law and exponential decay. I really don't see any difference between them. For ...

I am studying for college finals and I cannot solve the inequation (x-1)/(x-5)<0 using the method the professor taught us, which I have to use in the e...

Matrix A $\in$ $\mathbb{R}^{n\times n}$ is idempotent if $A^{2} = A$. Describe the Jordan form of A. How do I do this? I am able to decompose a matrix to ...

If we place the sphere so that its center is at the origin, then the plane $P_x$ intersects the sphere in a circle whose radius is $y = \sqrt{r^2-x^2}$.So...

I tried to figure this out the other day, but failed to arrive at a formula. It seems like a simple problem, though. Forgive me if my use of terminology s...