query: Verification of solution for $\lim_{x\to 1} \frac{x\cdot \sin\{x\}}{x-1}$
positive_passages.docid: 21670
positive_passages.text: Why does an infinite limit not exist?
negative_passages.docid: 78393
negative_passages.text: Find the limit $\lim_{n\to\infty} \frac{x_1 y_n + x_2 y_{n-1} + \cdots + x_n y_1}{n}$
negative_passages.docid: 74204
negative_passages.text: Evaluate $\lim_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
negative_passages.docid: 150734
negative_passages.text: Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.
negative_passages.docid: 30181
negative_passages.text: Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
negative_passages.docid: 122301
negative_passages.text: Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$
negative_passages.docid: 107386
negative_passages.text: Compute $\lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx$
negative_passages.docid: 74684
negative_passages.text: $\lim_{x \to 0} {1-x\cot x\over x^2}$
negative_passages.docid: 11382
negative_passages.text: Limit $\lim\limits_{x\to0}\frac1{\ln(x+1)}-\frac1x$
negative_passages.docid: 15822
negative_passages.text: Value of $\lim_{n\to \infty}\frac{1^n+2^n+\cdots+(n-1)^n}{n^n}$
negative_passages.docid: 7727
negative_passages.text: Convergence of series $\sum_{n=1}^\infty\sin(n)\cdot\sin(1/n)$
negative_passages.docid: 63289
negative_passages.text: Does $\sum\limits_{x=1}^\infty\sin(x)$ converge?
negative_passages.docid: 138583
negative_passages.text: What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$
negative_passages.docid: 113913
negative_passages.text: using L'Hospital solve $\lim_{x \to \infty} x - x^{2}\ln(1 + \frac{1}{x})$
negative_passages.docid: 151329
negative_passages.text: Showing $\lim_{(x,y) \to (0,0)} \sin (xy) / xy = 1$
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: 109718
negative_passages.text: Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)?