query: Trigonometric tough limit: $\lim\limits_{x\to 0} \frac{1-\cos x}{x^2}$
positive_passages.docid: 77669
positive_passages.text: Limits of trig functions
negative_passages.docid: 9746
negative_passages.text: Determine the following limit as x approaches 0: $\frac{\ln(1+x)}x$
negative_passages.docid: 41419
negative_passages.text: Solution of limit $\lim\limits_{x\to 0} \frac {e^{-1/x^2}}{x} $
negative_passages.docid: 4644
negative_passages.text: Finding the limit $\lim \limits_{n \to \infty}\ (\cos \frac x 2 \cdot\cos \frac x 4\cdot \cos \frac x 8\cdots \cos \frac x {2^n}) $
negative_passages.docid: 95508
negative_passages.text: Evaluate $\lim\limits_{x\to 1}\frac{\sqrt x-x^2 }{1-\sqrt x}$
negative_passages.docid: 86634
negative_passages.text: How to find $ \lim_{(x,y)\to(0,0)} \frac{\sin^2 (x-y)}{|x|+|y|} $?
negative_passages.docid: 41659
negative_passages.text: Limit as $x\to 0$ of $x\sin(1/x)$
negative_passages.docid: 22709
negative_passages.text: Show that $\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0$.
negative_passages.docid: 158447
negative_passages.text: Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$
negative_passages.docid: 64628
negative_passages.text: Solving limits of a sine wave $\lim_{x\to+\infty}\frac{\sin(x)}{x}$
negative_passages.docid: 46736
negative_passages.text: Limits involving trigonometric functions $f(x)=\lfloor{x^2 \rfloor} \sin^2(\pi x)$
negative_passages.docid: 82968
negative_passages.text: Find $(a,b)$ such that $\lim\limits_{x\to 0}\frac{f(x)}{x}=1$ implies $\lim\limits_{x\to 0}\frac{x(1+a\cos x)-b\sin x}{(f(x))^3}=1$
negative_passages.docid: 119469
negative_passages.text: Find the limit of $\lim\limits_{(x,y)\to (0,0)} \frac{x^2y^2}{x^2y^2+(x-y)^2}$
negative_passages.docid: 91278
negative_passages.text: The limit for $x\to 0$ of $x^3\sin (x)$ exists
negative_passages.docid: 70086
negative_passages.text: Limit without l'Hopital or Taylor series: $\lim\limits_{x \to 0} \frac{x\cos x- \sin x}{x^3}$
negative_passages.docid: 133882
negative_passages.text: $\lim_{n\to \infty }\cos (\pi\sqrt{n^{2}-n})$ - second battle
negative_passages.docid: 51622
negative_passages.text: Evaluating $\lim\limits_{x\rightarrow0}\frac{e^{-1/x^2}}{x}$