New posts in Limits

$\lim\limits_{n\to\infty}n\big(\sum_{k=1}^n\frac{k^2}{n^3+kn}-\frac{1}{3}\big)$?

Prove that $\lim\limits_{x\to+\infty}f'(x)=\lim\limits_{x\to+\infty}f''(x)=0$

Evaluating $\lim_{x\to\infty}(\sqrt{x^2+1} - x)(x+1) $

Prove that limit doesn't exists at all

$\lim_{ x \to 0 } \frac{e-(1+\arctan x)^{\frac{1}{x}}}{x}$

Can any positive real be approximated as $2^m/3^n$ with $(m,n)$ large enough?

Derivative of Arctangent with definition of derivative

The proofs of limit laws and derivative rules appear to tacitly assume that the limit exists in the first place

$g(x) = \frac{f'(x)}{f(x)}$ not bounded

How to prove that this limit diverges?