query: Multivariable limit $\lim_{(x, y) \to (0, 0)} \frac{x \sin(x^2 y^2)}{x^2 + y^2}$
positive_passages.docid: 146180
positive_passages.text: Prove that $x\sqrt{1-x^2} \leq \sin x \leq x$
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: 80720
negative_passages.text: What paths to choose to prove that $\lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 - y^2}$ does not exist?
negative_passages.docid: 136450
negative_passages.text: Compute $\lim_{x \rightarrow +\infty} \frac{[\int^x_0 e^{y^{2}} dy]^2}{\int^x_0 e^{2y^{2}}dy}$
negative_passages.docid: 12375
negative_passages.text: Prove $\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$
negative_passages.docid: 64281
negative_passages.text: Computing A Multivariable Limit: $\lim_{(x,y) \to (0,0)}\frac{2x^2y}{x^4 + y^2}.$
negative_passages.docid: 38804
negative_passages.text: Wrong Wolfram|Alpha limit? $ f(x,y) = \frac {xy}{|x|+|y|} $ for $(x,y)\to(0,0)$
negative_passages.docid: 102408
negative_passages.text: Evaluate the limit $\lim_{x \to 0}{\frac{\sqrt{1+x\sin{x}}-\sqrt{\cos{2x}}}{\tan^{2}{\frac{x}{2}}}}$
negative_passages.docid: 127767
negative_passages.text: How to find $\lim_{(x,y)\rightarrow (0,0)} \frac{\sin(x\cdot y)}{x}$?
negative_passages.docid: 67429
negative_passages.text: Solve $\lim_{x\to0}{\frac{x^2\cdot\sin\frac{1}{x}}{\sin x}}$
negative_passages.docid: 98392
negative_passages.text: Value of the limit $\lim_{x \to 0} \frac{\sin(\frac{1}{x})}{\sin(\frac{1}{x})}$
negative_passages.docid: 113336
negative_passages.text: Limit of $(\frac{1}{n^2})^{(\frac{1}{n})}$
negative_passages.docid: 101130
negative_passages.text: How to determine the limit of $ f(x, y)=\frac{9xy}{x^2 + y^2}$?
negative_passages.docid: 17069
negative_passages.text: Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$
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: 68136
negative_passages.text: $\lim\limits_{x\to 0} \frac{\tan x - \sin x}{x^3}$?
negative_passages.docid: 115819
negative_passages.text: Evaluate $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n})$