query: Evaluate limit integrate: $\lim_{n \rightarrow +\infty}{\int_{0}^{\frac {\pi}{2}} \sin^{n} x dx}$
positive_passages.docid: 17779
positive_passages.text: Proving the Limit of a Sequence of without the Dominated Convergence Theorem
negative_passages.docid: 95718
negative_passages.text: Computing $ \lim_{n\rightarrow \infty}\left(\frac{1^n+2^n+\cdots \cdots +n^n}{n^n}\right)$
negative_passages.docid: 70742
negative_passages.text: Evaluate $\lim_{x\rightarrow 0} \frac{\sin (6x)}{\sin(2x)}$ without L'Hopital
negative_passages.docid: 98365
negative_passages.text: How to evaluate $\lim_{x \rightarrow \infty} \left(\left(\frac{x+1}{x-1}\right)^x -e^2\right){x}^2$
negative_passages.docid: 20843
negative_passages.text: Evaluate the limit of $\lim_{n\to\infty}\frac{1}{n^2}\left(\frac{2}{1}+\frac{9}{2}+\frac{64}{9}+\cdots+\frac{(n+1)^{n}}{n^{n-1}}\right)$
negative_passages.docid: 33675
negative_passages.text: Find $\lim_{n\to \infty} \int_n^{n+1} {\sin x \over x} dx$
negative_passages.docid: 144719
negative_passages.text: How to find $\lim\limits_{n\rightarrow \infty}\frac{(\log n)^p}{n}$
negative_passages.docid: 151149
negative_passages.text: $\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
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: 17019
negative_passages.text: Show that: $\lim\limits_{r\to\infty}\int\limits_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta=0$
negative_passages.docid: 109171
negative_passages.text: How to evaluate this trigonometric limit?
negative_passages.docid: 82831
negative_passages.text: Evaluating the limit $\lim_{n\to\infty} \left[ \frac{n}{n^2+1}+ \frac{n}{n^2+2^2} + \ldots + \frac{n}{n^2+n^2} \right]$
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: 93155
negative_passages.text: Evaluate $\mathop {\lim }\limits_{x \to 0} \left( {{1 \over {{{\sin }^2}x}} - {1 \over {{x^2}}}} \right)$
negative_passages.docid: 24076
negative_passages.text: Evaluating limit (iterated sine function)
negative_passages.docid: 49029
negative_passages.text: Find the limit $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{1}{k+n}$
negative_passages.docid: 1234
negative_passages.text: Evaluating limits of integrals