Can anyone provide some techniques for solving this kind of problem? Many thanks.

a) Given that exactly one head occurred, what is the probability that it occurred on the first toss. I have this so far, and I just need help computing th...

The question is : $\dfrac{\csc x}{\sec x} = \cot x$ After solving a bit I get $$\frac{\frac1{\sin x}}{\frac1{\cos x}} = \frac{\cos x}{\sin x}$$ $$\frac{\c...

I am trying to study for a test and the teacher suggest we memorize $\sin(A+B)$, $\sin(A-B)$, $\cos(A+B)$, $\cos (A-B)$, and then be able to derive the re...

Solve $\sin(x)=1$ for values of $x$ where $-2\pi\le x\le 2\pi$ Now, I know that $sin(\pi/2$)=$1$ in 1st quadrant and by using $sin(\pi-x)=sin(x) $ I still...

Prove that $T$ is a normal operator if and only if $\|{Tv}\|^2 = \|{T^*v}\|^2$ for every vector $v \in V$ $(\Rightarrow)$ $T$ is normal, so we have $TT^* ...

So I recently read this question: Difference between improper node and proper node for phase portrait and I find myself still needing some more concrete c...

Hi everyone I wonder to myself if the next proof is correct. I would appreciate any suggestion. Proposition: There is not a sequence of natural numbers wh...

Here's a homework question I'm struggling with: Let $p(x),q(x)$ two polynomials (such that $q(x) \ne 0$). Prove that $$\lim_{x \to 0}e^{-1/x^2} ...

Consider we have the $100$ distinct integers between $1$ and $100$ inclusive. The median and fiftyth percentile can be calculated as below. Ordering: $1,2...