Proof of $\displaystyle\lim_{x‎\to‎ 0} \frac{e - (1+x)^\frac{1}{x}}{x}=\frac{e}{2}$
19263
Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$
58041
Prove by Mean Value Theorem $\frac{x}{1+x}0$
37489
Show that $ \lim_{(x,y) \to 0} \frac {|x|^ \alpha |y|^ \beta} {|x|^ \gamma + |y|^ \delta} \text {exists} \iff \alpha/\gamma + \beta/\delta > 1.$
53109
Why is this limit $\lim_{n \to \infty}(1 + \frac{1}{n})^n$ equal to $e$?
67645
Prove that $\displaystyle{\lim_{n \to \infty}a_n ^{1/k}}= a^{1/k}$ if $a_n \ge 0$ for all $n$ and $\displaystyle{\lim_{n \to \infty}a_n}= a$
53236
Formal proof of $\lim_{x\to a}f(x) = \lim_{h\to 0} f(a+h)$
108630
Showing that $\displaystyle\lim_{s \to{1+}}{(s-1)\zeta(s)}=1$
111929
Find the limit: $\lim_\limits{x\to 0}{\frac{\left(1+x\right)^{1/x}-e}{x}}$
5436
How to prove $\lim \limits_{x \to 1^-} \sum\limits_{n=0}^\infty (-1)^nx^{n²} = \frac{1}{2} \ $?
43852
Evaluate $\lim_{x\to 0}\frac{e^{(x+1)^{1/x}}-(x+1)^{e/x}}{x^2}$
53719
Evaluate $\lim_{x \to 0} \left(\frac{1}{\ln(1+x)} + \frac{1}{\ln(1-x)}\right)$
142249
Show that $\lim_{n\to \infty} \int_E \cos^2(nx + a_n) dx = \frac{1}{2}m(E)$
116257
How to show $\lim_{k\rightarrow \infty} \left(1 + \frac{z}{k}\right)^k=e^z$
57203
Prove that $\lim_{x \to \infty}\big(\frac{x}{x-1}\big)^x$ is also $e$.
108405
Prove that $\lim\limits_{n\to\infty}1 + \frac{1}{1!} + \frac {1}{2!} + \cdots + \frac{1}{n!}\ge\lim\limits_{n\to\infty}(1+\frac{1}{n})^n$
6382
Showing $\frac{x}{1+x}0$ using the mean value theorem
1057
How prove this integral limit $=f(\frac{1}{2})$