query: $\lim_{x \to 0}\frac{x- \sin{x}}{x^2}$
positive_passages.docid: 150734
positive_passages.text: Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.
negative_passages.docid: 79299
negative_passages.text: Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$
negative_passages.docid: 36063
negative_passages.text: Finding the limit of $(1-\cos x)/x^2$
negative_passages.docid: 126578
negative_passages.text: Evaluate $\lim_{(x,y)\to(0,0)}\frac{\cos(xy)-1}{x^2y^2}$
negative_passages.docid: 149102
negative_passages.text: Evaluating $\lim_{x \to 0} x\sin\left(\frac{1}{x}\right)$ or showing it does not exist
negative_passages.docid: 125088
negative_passages.text: show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
negative_passages.docid: 109540
negative_passages.text: Simplify limit problem $\lim\limits_{x\to 0}\frac{\sqrt{2+x^2}-\sqrt{2+x^2}}{x^2}$
negative_passages.docid: 65975
negative_passages.text: Calculating $\lim_{n\to\infty}\sqrt{n}\sin(\sin...(\sin(x)..)$
negative_passages.docid: 64001
negative_passages.text: What is the result of $\lim\limits_{x \to 0}(1/x - 1/\sin x)$?
negative_passages.docid: 36648
negative_passages.text: The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$
negative_passages.docid: 41659
negative_passages.text: Limit as $x\to 0$ of $x\sin(1/x)$
negative_passages.docid: 45728
negative_passages.text: Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
negative_passages.docid: 7819
negative_passages.text: Calculate: $ \lim_{x \to 0 } = x \cdot \sin(\frac{1}{x}) $
negative_passages.docid: 65239
negative_passages.text: Find $\lim_{x \to 0} \frac{x - \tan(x)}{x - \sin(x)}$
negative_passages.docid: 37755
negative_passages.text: Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$
negative_passages.docid: 39798
negative_passages.text: Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?
negative_passages.docid: 22709
negative_passages.text: Show that $\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0$.