Use depth-first search to produce a spanning tree for the given simple graph. Choose $a$ as the root of this spanning tree. Here is answer and I am not su...

ABCD is a square. C' is a point on BA and B' is a point on AD such that BB' and CC' are perpendicular. Show that BB' = CC' I...

I'm working on a proof for analysis: "Let $\{x_n\}$ be a convergent sequence in $\mathbb R^d$ with limit $x$. Set $$A=\{x_1,x_2,x_3,\cdots\}\cup\{x\}...

Levy's continuity theorem says that if a sequence of random variables $X_{i}$ has characteristic functions $\phi_{X_i}$ converging pointwise to a cha...

Suppose you have the series: $$\sum_{n=1}^\infty (-1)^n\ln(n)$$ Does it converge or diverge? You cannot apply the alternating series test since $b_n$ is n...

I am self learning abstract algebra. I want to know which theorems are a must to understand. Now these are limits I have to deal with (please consider whe...

So I am wrapping up a College Algebra course from my local community college and am scheduled to start the first semester of a two semester precalculus co...

The question asks to find the derivative of the function $1-\cos(x)\sin(x)$, and I thought maybe using some derivative rules I could, but I don't kno...

For compass and straightedge problems, you could have a line between two points A and B, and want to make a line the same size between C and line DE. If y...

In addition to the common integration shortcut of $\int x \cdot e^{ax}=\frac{xe^{ax}}{a}-\frac {e^{ax}}{a^2}+c$ Is there supplemental shortcut that can he...