Limit of an integral $\lim_{n\to \infty}\int_{1385}^{2017}f(nx)\,dx $
10308
Undergraduate math competition problem: find $\lim \limits_{n \to \infty} \int \limits^{2006}_{1385}f(nx)\, \mathrm dx$
95397
Finding out the limit $\lim_{a \to \infty} \frac{f(a)\ln a}{a}$
3200
Limit of integral without Taylor expansion
97747
Limit of $\lim\limits_{n\to\infty} (1 + \frac{x_n}{n})^n$
103513
Show that $\lim_{n\to \infty}\int_{-\pi}^{\pi}f(x)g(nx)\,dx=\frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)\,dx\int_{-\pi}^{\pi}g(x)\,dx$
65015
Computing $\lim_{n \to \infty} \sqrt[n]{ \int_{0}^{1} (1+x^n)^n dx}$
90558
A question related to a convergence of an integral
111279
The value of $\lim_{n \to \infty}\int_{0}^{1}nx^ne^{x^2}dx$
68368
Evaluate $\lim_{n \to \infty} \int_{0}^1 [x^n + (1-x)^n ]^{1/n} \ \mathrm{d}x$
41203
Finding $\lim\limits_{x \to \infty} (\sqrt{9x^2+x} - 3x)$
20404
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
45806
Finding $\lim\limits_{n \rightarrow \infty}\left(\int_0^1(f(x))^n\,\mathrm dx\right)^\frac{1}{n}$ for continuous $f:[0,1]\to[0,\infty)$
154286
Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
91290
Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$
24056
Convergence of the improper integral $\int_{0}^{\pi/2}\tan^{p}(x) \; dx$
32853
Computing $\lim_{A\to\infty} \frac{1}{A} \int\limits_1^A \! A^{\frac{1}{x}} \, \mathrm{d}x.$