query: How do I compute the limit of this integral: $\lim_{n\to\infty}\int_{0}^{\infty}\frac{\sin(\frac{x}{n})}{(1+\frac{x}{n})^{n}}dx$?
positive_passages.docid: 156231
positive_passages.text: Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
negative_passages.docid: 150981
negative_passages.text: Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?
negative_passages.docid: 86169
negative_passages.text: How do I solve this limit: $\lim _{x \to 0} \left(\frac{ \sin x}{x}\right)^{1/x}$?
negative_passages.docid: 11489
negative_passages.text: Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
negative_passages.docid: 41366
negative_passages.text: Compute $\lim\limits_{n\to\infty} \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)^{{1}/{2}}\cdots\left(1+\frac{n}{n}\right)^{{1}/{n}}$
negative_passages.docid: 88925
negative_passages.text: How find this limit $\lim\limits_{x\to 0^{+}}\frac{\sin{(\tan{x})}-\tan{(\sin{x})}}{x^7}$
negative_passages.docid: 64628
negative_passages.text: Solving limits of a sine wave $\lim_{x\to+\infty}\frac{\sin(x)}{x}$
negative_passages.docid: 154605
negative_passages.text: How to compute $\lim\limits_{n\rightarrow \infty} \{(2+\sqrt{3})^{n}\}$, where $\{x\}$ is the fractional part of $x$?
negative_passages.docid: 44054
negative_passages.text: Evaluating the integral $\mathop{\lim}\limits_{n \to \infty} \int_{-1}^{1} f(t)\cos^{2}(nt) \ dt $
negative_passages.docid: 65337
negative_passages.text: Compute $\int_{0}^{\infty}\frac{x\sin 2x}{9+x^{2}} \, dx$
negative_passages.docid: 89263
negative_passages.text: Find the limit $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k+n}$
negative_passages.docid: 117542
negative_passages.text: Finding the limit $\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$
negative_passages.docid: 41515
negative_passages.text: fine the limit : $\lim_{ n \to \infty }\frac{1}{n}\int_{0}^{n}{ \frac{x\ln(1+\frac{x}{n})}{1+x}}=?$
negative_passages.docid: 57224
negative_passages.text: Compute $\int_0^\infty \frac{dx}{1+x^3}$
negative_passages.docid: 73786
negative_passages.text: Limit of $\frac{\sin(x+y)}{x+y}$ as $(x,y) \to (0,0)$
negative_passages.docid: 84788
negative_passages.text: Find limit of $\lim_{x\to 0}\frac{\sin^{200}(x)}{x^{199}\sin(4x)}$, if it exists
negative_passages.docid: 33372
negative_passages.text: What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$?