query: How to find $\lim\limits_{x\to0}\frac{x^2+2\cos x-2}{x \sin^3x}$
positive_passages.docid: 156610
positive_passages.text: To prove the limit of $\frac{x^2+2\cos x-2}{x\sin^3 x}$ at zero is $1/12$
negative_passages.docid: 65275
negative_passages.text: Finding $\lim\limits_{x\to1^-}\Bigl(\prod\limits_{n=0}^{\infty}\Bigl(\frac{1+x^{n+1}}{1+x^n}\Bigr)^{x^n}\Bigr)$
negative_passages.docid: 20773
negative_passages.text: Find $\lim\limits_{n \to \infty} \frac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$.
negative_passages.docid: 126578
negative_passages.text: Evaluate $\lim_{(x,y)\to(0,0)}\frac{\cos(xy)-1}{x^2y^2}$
negative_passages.docid: 31776
negative_passages.text: How to find $\lim_{x\to 0}\frac{\tan 3x}{\tan 5x}$?
negative_passages.docid: 126211
negative_passages.text: How to compute $\lim _{x\to 0}\frac{x\bigl(\sqrt{3e^x+e^{3x^2}}-2\bigr)}{4-(\cos x+1)^2}$?
negative_passages.docid: 103218
negative_passages.text: Find $\lim_{(x,y) \to (0,0)} \frac{\tan(x^3+y^3)}{\sin(x^2+y^2)}$
negative_passages.docid: 28161
negative_passages.text: Solve $\lim_{x\to 0} \frac{\sin x-x}{x^3}$
negative_passages.docid: 2167
negative_passages.text: Find the limit $\lim\limits_{x\to \infty}(e^{-x}+2\cos3x)$, or show that it does not exist.
negative_passages.docid: 139215
negative_passages.text: Find the value of $\lim_{x \to - \infty} \left( \sqrt{x^2 + 2x} - \sqrt{x^2 - 2x} \right)$
negative_passages.docid: 125087
negative_passages.text: Evaluate the limit of ratio of sums of sines (without L'Hopital): $\lim_{x\to0} \frac{\sin x+\sin3x+\sin5x}{\sin2x+\sin4x+\sin6x}$
negative_passages.docid: 156231
negative_passages.text: Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
negative_passages.docid: 65239
negative_passages.text: Find $\lim_{x \to 0} \frac{x - \tan(x)}{x - \sin(x)}$
negative_passages.docid: 79684
negative_passages.text: Finding $\lim \limits_{x \to 0} \frac{1 - \cos x}{x}$, given $\lim \limits_{x \to 0} \frac{\sin x}{x} = 1$
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: 64628
negative_passages.text: Solving limits of a sine wave $\lim_{x\to+\infty}\frac{\sin(x)}{x}$
negative_passages.docid: 129011
negative_passages.text: Is there limit $ \lim_{(x,y) \to (0,0)} \frac{x^3}{x^2 + y^2}$?