Apologies if there is a duplicate somewhere; I couldn't find one. The use of the root "deriv" in the context of differentiation seems odd: we have di...

Vieta's theorem states that given a polynomial $$ a_nx^n + \cdots + a_1x+a_0$$ the quantities $$\begin{align*}s_1&=r_1+r_2+\cdots\\ s_2&=r_1 ...

The book I'm reading doesn't explicitly give a definition of separable metric spaces. The only type of separability definition I know that a sep...

Let $r(t) = (t^2, t, t^4)$. Find normal plane at point t = 1. While working on this problem I have come to point where I am not sure what to do. I origina...

Sorry if this is a silly question but most books claim $\log n < n$ for $n \geq 1$ without providing any proof, saying it's too obvious. Could som...

I'm not very good at this, so hopefully I'm not making a silly mistake here... Assuming that $\infty$ is larger than any real number, we can the...

Evaluate the volume of $V\subset \mathbb{R}^3$, which is bounded by paraboloid $z=1-x^2-y^2$ and the surface $z=1-y,$ for $z\geqslant 0.$ Attempt. The des...

I am new to vector calculus and found this problem in the textbook which I am not sure how to work with, but I want to learn to do so: Show details to fin...

Are there any useful identities for quickly calculating the sum of consecutive logs? For example $\sum_{k=1}^{N} log(k)$ or something to this effect. I sh...

This is my first question on the Mathematics section of StackExchange, so please forgive me if I don't follow all the rules or things like that. Here...