Limit of integral of $\frac{2nx^{n-1}}{1+x},\, x\in [0,1]$
11489
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
146349
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
146663
Limit $\lim_{n \to \infty} \frac {a_n}{2^{n-1}}=\frac 4{\pi}$ for $a_{n+1}=a_n+\sqrt{1+a_n^2}$ and $a_0=0$
5402
Prove or the disprove the existence of a limit of integrals
154286
Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
74204
Evaluate $\lim_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
44668
Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$
1234
Evaluating limits of integrals
19263
Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$
103513
Show that $\lim_{n\to \infty}\int_{-\pi}^{\pi}f(x)g(nx)\,dx=\frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)\,dx\int_{-\pi}^{\pi}g(x)\,dx$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
68241
Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
44054
Evaluating the integral $\mathop{\lim}\limits_{n \to \infty} \int_{-1}^{1} f(t)\cos^{2}(nt) \ dt $
30160
How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$?
15822
Value of $\lim_{n\to \infty}\frac{1^n+2^n+\cdots+(n-1)^n}{n^n}$
70790
Evaluation of $\lim_{q \to 0} (\int_0^1 |f|^q)^{1/q} $ for $f \in L^1([0,1])$.
49128
How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$?