Finding value of $\lim _{n\to\infty} \int_0^\pi \frac{\sin x}{1+\cos^2(nx)}dx$
91290
Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$
64480
How do I find $\int_{0}^{\infty} \frac{\sin^4 x}{x^2}\,dx$?
25193
Find $ \lim _{n\to \infty} \frac{n^1+\dots+n^n}{1^n+\dots+n^n}$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
50243
Find $\lim_{n \to +\infty} \frac{1}{n}\sqrt[n]{\frac{(2n)!}{n!}} $ using Riemann integral
7
Find value of the limit: $\lim_{n\to \infty}\sqrt[n]{1^2+2^2+\cdots+n^2}$
28461
Show that $\lim_{n\to\infty} \sum_{k=1}^{n} \frac{n}{n^2+k^2}=\frac{\pi}{4}$
86843
Find the value of : $\lim_{n\to\infty}[(n+1)\int_{0}^{1}x^{n}\ln(1+x)dx]$.
107386
Compute $\lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx$
111279
The value of $\lim_{n \to \infty}\int_{0}^{1}nx^ne^{x^2}dx$
86634
How to find $ \lim_{(x,y)\to(0,0)} \frac{\sin^2 (x-y)}{|x|+|y|} $?
24022
Compute $\int _0 ^{2\pi} (\sum_{n=1}^\infty \frac {\cos(nx)}{2^n})^2 dx$
37260
Calculate $\lim_{n\to{+}\infty}{(\sqrt{n^{2}+n}-n)}$
129913
Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
142708
Finding the limit $\lim_{n\rightarrow\infty}(1-\frac{1}{3})^2(1-\frac{1}{6})^2(1-\frac{1}{10})^2...(1-\frac{1}{n(n+1)/2})^2$
65975
Calculating $\lim_{n\to\infty}\sqrt{n}\sin(\sin...(\sin(x)..)$