Why is $e = \lim\limits_{x\to 0} (1+x)^\frac{1}{x}$?
115028
If $e=\lim\limits_{x\to \infty} (1+x^{-1})^x$, why doesn't $e=1$?
67894
$\epsilon$-$\delta$ proof that $\lim\limits_{x \to 1} \frac{1}{x} = 1$.
13533
Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
101687
$ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $
119200
When does $\lim_{n\to\infty}f(x+\frac{1}{n})=f(x)$ a.e. fail
36648
The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$
6619
Prove that $\lim \limits_{(x,y,z) \to (0,0,0)} \frac{{xyz}}{{x+y+z}}=0$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
114675
Evaluating $\lim\limits_{x\to 0}(1+x)^{1/x}$?
57203
Prove that $\lim_{x \to \infty}\big(\frac{x}{x-1}\big)^x$ is also $e$.
27511
Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$
111929
Find the limit: $\lim_\limits{x\to 0}{\frac{\left(1+x\right)^{1/x}-e}{x}}$
148170
Difficulty in evaluating a limit: $\lim_{x \to \infty} \frac{e^x}{\left(1+\frac{1}{x}\right)^{x^2}}$
46990
$\lim_{x\to0}\frac{e^x-1-x}{x^2}$ using only rules of algebra of limits.
135731
Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
132738
Showing $\lim_{n \to \infty} m(E_n) = 0$, assuming $f > 0$ a.e. and $\lim_{n \to \infty} \int_{E_n}f \,dm =0$
74919
Finding limit of function $\lim_{x\to 0}\left(\frac{(1+x)^\frac1x}{e}\right)^\frac1x$