query: Prove: $\lim\limits_{(x,y)\to (0,0)}\frac{xy}{(x^2+y^2)^\frac12}=0$
positive_passages.docid: 146640
positive_passages.text: Computing $\lim_{(x,y)\to (0,0)}\frac{x+y}{\sqrt{x^2+y^2}}$
negative_passages.docid: 62209
negative_passages.text: Finding multivariable limits for the function $\frac{3x^2y}{x^2+y^2}$
negative_passages.docid: 80373
negative_passages.text: How to prove that $\lim_{n \to\infty} \frac{(2n-1)!!}{(2n)!!}=0$
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: 111205
negative_passages.text: Proving that $\lim_{k\to \infty}\frac{f(x_k)-f(y_k)}{x_k-y_k}=f'(c)$ where $\lim_{k\to \infty}x_k=\lim_{k\to \infty}y_k=c$ with $x_k<c<y_k$
negative_passages.docid: 50537
negative_passages.text: Prove $\lim_{x\to0}\sqrt{4-x}=2$ using the precise definition of limits. (Epsilon-Delta)
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: 130766
negative_passages.text: Prove $\lim\limits_{n\to\infty}na_n\ln(n)=0$
negative_passages.docid: 12083
negative_passages.text: How to prove $\limsup (x_{n}+y_{n})=\lim x_{n}+\limsup y_{n}$?
negative_passages.docid: 45360
negative_passages.text: How to obtain $\lim_{(x,y) \to (0,0)} (x^2·y^3)/(x^4+y^6)$
negative_passages.docid: 126578
negative_passages.text: Evaluate $\lim_{(x,y)\to(0,0)}\frac{\cos(xy)-1}{x^2y^2}$
negative_passages.docid: 18062
negative_passages.text: How can I prove $\lim_{n \to \infty} \frac{n^2}{2^n}=0$
negative_passages.docid: 30181
negative_passages.text: Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
negative_passages.docid: 106281
negative_passages.text: Prove $\lim\limits_{n\to \infty}\frac{1}{\sqrt n}\left|\sum\limits_{k=1}^n (-1)^k\sqrt k\right|= \frac{1}{2}$
negative_passages.docid: 117246
negative_passages.text: Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$.
negative_passages.docid: 39148
negative_passages.text: Does $\lim_{(x,y)\to(0,0)}[x\sin (1/y)+y\sin (1/x)]$ exist?
negative_passages.docid: 126256
negative_passages.text: Prove limit of function