query: Does $\lim_{x\to0}\left(\frac{\sin(x)}{x}\right)^{\frac{1}{x^2}} =0$?
positive_passages.docid: 85249
positive_passages.text: Evaluating: $\lim\limits_{x\to0}\left(\frac{\sin x}{x}\right)^{{6}/{x^{2}}}$
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: 20956
negative_passages.text: Correct way to prove the limit: $\mathop {\lim }\limits_{x \to 0} {x^\alpha }\int\limits_x^1 {\frac{{f\left( t \right)}}{{{t^{\alpha  + 1}}}}dt} $?
negative_passages.docid: 40487
negative_passages.text: Given $\lim_{x \rightarrow a}f(x)+\frac1{\left|f(x)\right|}=0$, what is $\lim_{x \rightarrow a}f(x)$?
negative_passages.docid: 63165
negative_passages.text: Is this limit correct: $\lim_{x \to+\infty} \frac{\log_{2}(x-1)}{x} = 0$?
negative_passages.docid: 13104
negative_passages.text: What is $\lim_{x \to \infty} \frac{\sin x}{\sin x}?$
negative_passages.docid: 97326
negative_passages.text: Find $\lim_{x \to 0} (\frac{\tan(x)}{x})^{\frac{1}{x}}$
negative_passages.docid: 56085
negative_passages.text: Calculate the limit : $\lim_{x \to 0}\frac{x-\sin{x}}{x^3}$ WITHOUT using L'Hopital's rule
negative_passages.docid: 7819
negative_passages.text: Calculate: $ \lim_{x \to 0 } = x \cdot \sin(\frac{1}{x}) $
negative_passages.docid: 23489
negative_passages.text: Limit of $\left(1+\frac{a}{x}\right)^x$ with and without L'Hôpital's rule
negative_passages.docid: 72036
negative_passages.text: Closed form of $\int_0^\infty \sin(x)\sin\left(\frac{1}{x}\right)dx$?
negative_passages.docid: 129011
negative_passages.text: Is there limit $ \lim_{(x,y) \to (0,0)} \frac{x^3}{x^2 + y^2}$?
negative_passages.docid: 80314
negative_passages.text: Finding $\lim\limits_{x\to 0}\frac{\sin{3x}}{x}$
negative_passages.docid: 149376
negative_passages.text: How to Find $ \lim\limits_{x\to 0} \left(\frac {\tan x }{x} \right)^{\frac{1}{x^2}}$.
negative_passages.docid: 110126
negative_passages.text: Prove that $\lim\limits_{(x,y) \to (0,0)} \frac{{x{y^2}}}{{{x^2} + {y^4}}} = 0$
negative_passages.docid: 19791
negative_passages.text: Calculating $\lim_{x\to0} \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$
negative_passages.docid: 40463
negative_passages.text: Evaluating $\lim _{x\to 1}\left(\frac{\sqrt[3]{x}-1}{2\sqrt{x}-2}\right)$