Proof that $\lim_{x\to\infty}\left(\frac{x}{x-1}\right)^x=e$.
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
137609
Proving $\lim_{n\rightarrow\infty} n(2^{1/n} - 1) = \log 2$
135731
Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
142249
Show that $\lim_{n\to \infty} \int_E \cos^2(nx + a_n) dx = \frac{1}{2}m(E)$
53109
Why is this limit $\lim_{n \to \infty}(1 + \frac{1}{n})^n$ equal to $e$?
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
144403
Limit $\lim_{x\rightarrow +\infty}\sqrt{x}e^{-x}\left(\sum_{k=1}^{\infty}\frac{x^{k}}{k!\sqrt{k}}\right)$
16739
The Limit of $x\left(\sqrt[x]{a}-1\right)$ as $x\to\infty$.
104853
Proving that $\lim\limits_{n\to\infty}n\left( \int_0^1 f(t)\, dt -\frac1n\sum_{k=0}^{n-1}f\left(\frac k n\right) \right)=\frac{f(1)-f(0)}{2}$
54830
Find the limit $\lim\limits_{x\to\infty} f(x)= \lim\limits_{x \to \infty} \left(\frac{x}{x+1}\right)^x$
17329
How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?
52545
Prove limit converges in definition of $e.$
91523
Prove this limit as $x\to\infty$
140790
Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.
113289
finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$
27511
Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$
79024
the derivation of E(X|X)