Applying L'Hopital's rule for $\lim_{x\to\infty} x((1+1/x)^x-e)$
33701
Find this limit using L`Hopitals rule
57203
Prove that $\lim_{x \to \infty}\big(\frac{x}{x-1}\big)^x$ is also $e$.
44668
Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$
95962
proving a theorem from limit using Hopital rule
90431
Compute $\lim_{x\to 0} \frac{e^{-1/x^2}}{x}$ without using L'Hopital?
30834
limit of $\lim\limits_{x \to \infty}((x+1)^a - x^a)$
113913
using L'Hospital solve $\lim_{x \to \infty} x - x^{2}\ln(1 + \frac{1}{x})$
111636
Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$
71743
$\lim (1+\frac{1}{n+1})^n = e$
127107
Evaluate $\lim_{x\to \infty}\ (x!)^{1/x}$
144422
How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
27511
Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$
101716
Find this limit: $ \lim_{n \to \infty}{(e^{\frac{1}{n}} - \frac{2}{n})^n}$
19263
Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$
68368
Evaluate $\lim_{n \to \infty} \int_{0}^1 [x^n + (1-x)^n ]^{1/n} \ \mathrm{d}x$
148898
Limit $(0÷0)$ and use L'hopital Rule
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$