Evaluate: $\lim_{n\to \infty}\sqrt{n}\int_{0}^1 \frac{1}{(1+x^2)^{n}}dx$
19631
Finding $\lim_{n\to \infty}\sqrt n \int_0^1 \frac{\,dx}{(1+x^2)^n}$
66526
Find the limit of: $\lim_{n\to\infty} \frac{1}{\sqrt[n+1]{(n+1)!} - \sqrt[n]{(n)!}}$
136297
Evaluate $\lim_{x \to 1} \frac{\sqrt[3]{x} -1}{\sqrt{x} -1}$
41115
$\text{Evaluate:} \lim_{b \to 1^+} \int_1^b \frac{dx}{\sqrt{x(x-1)(b-x)}}$
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
98365
How to evaluate $\lim_{x \rightarrow \infty} \left(\left(\frac{x+1}{x-1}\right)^x -e^2\right){x}^2$
101536
Difficult limit evaluation: $\lim_{x\to\infty}(\sqrt{x^2+4x} - x)$
100401
Evaluate $\int \frac{1}{(x^2+1)^2}dx$
156546
Evaluate the limit $\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}\left(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n}}\right)$
124426
Help in evaluating: $\lim_{n \to \infty} \frac{\sum_{k=1}^n\lfloor kx\rfloor}{n^2} $
81090
Calculate $\lim_{n\to\infty}(\sqrt{n^2+n}-n)$.
4224
Evaluate limit of an integral: $\lim_{x\to \infty }\frac{1}{x}\int _0^x\:\frac{dt}{2+\cos t}$
8387
Evaluate $\lim_{n \rightarrow \infty} \frac {[(n+1)(n+2)\cdots(n+n)]^{1/n}}{n}$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
155873
Evaluate $\lim\limits_{n\rightarrow \infty}\frac{n+n^2+n^3+\cdots +n^n}{1^n+2^n+3^n+\cdots +n^n}.$
102408
Evaluate the limit $\lim_{x \to 0}{\frac{\sqrt{1+x\sin{x}}-\sqrt{\cos{2x}}}{\tan^{2}{\frac{x}{2}}}}$
154506
Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$