query: Show that $\lim \sin(xy)/xy =1$ when $(x,y)$ tends to $(0,0)$
positive_passages.docid: 151329
positive_passages.text: Showing $\lim_{(x,y) \to (0,0)} \sin (xy) / xy = 1$
negative_passages.docid: 41659
negative_passages.text: Limit as $x\to 0$ of $x\sin(1/x)$
negative_passages.docid: 114862
negative_passages.text: Find the limit $\displaystyle \lim_{x \to 0^+} (\sin x)^\frac1{\ln x}$
negative_passages.docid: 5478
negative_passages.text: Limit of $\lim_{(x,y)\rightarrow(0,0)}\frac{x^2y^2}{x^3+y^3}$
negative_passages.docid: 123248
negative_passages.text: How can I show $\lim_{n\to\infty}\prod_{j}^n\frac{\sin(jn^{-3/2}u)}{jn^{-3/2}u}=e^{-u^2/18}$?
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: 22598
negative_passages.text: When does the limit $\lim_{(x,y)\to(0,0)} \frac{x^ky^l}{x^{2p}+y^{2q}}$ exist?
negative_passages.docid: 112898
negative_passages.text: Derivative of sin(x)/x at $0$ by definition of derivative
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: 156355
negative_passages.text: Show that $\lim_{z \rightarrow \infty} -z^xe^{-z} = 0$
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: 1444
negative_passages.text: Prove/Show that Limit is equal to 0.
negative_passages.docid: 67853
negative_passages.text: Prove existence of $\lim_{(x,y) \rightarrow (0,2)} \frac{x (y-2)^3}{3x - 5(y-2)^4}$
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: 126578
negative_passages.text: Evaluate $\lim_{(x,y)\to(0,0)}\frac{\cos(xy)-1}{x^2y^2}$
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: 158447
negative_passages.text: Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$