query: Want to prove that: $\lim_{(x,y)\to\ (0,0)}xy\log(x^2+y^2)=0$
positive_passages.docid: 48935
positive_passages.text: Showing $\lim_{(x,y) \to (0,0)} xy \log(x^2+y^2) = 0$
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: 109907
negative_passages.text: How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$
negative_passages.docid: 35325
negative_passages.text: Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.
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: 67292
negative_passages.text: Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$
negative_passages.docid: 74835
negative_passages.text: how to prove that $ \lim x_n^{y_n}=\lim x_n^{\lim y_n}$?
negative_passages.docid: 92876
negative_passages.text: Prove that $ \lim (s_n t_n) =0$ given $\vert t_n \vert \leq M $ and $ \lim (s_n) = 0$
negative_passages.docid: 156355
negative_passages.text: Show that $\lim_{z \rightarrow \infty} -z^xe^{-z} = 0$
negative_passages.docid: 135664
negative_passages.text: Limit of $x \log x$ as $x$ tends to $0^+$
negative_passages.docid: 16948
negative_passages.text: Need help with a proof that if $xy=0$ then $x=0$ or $y=0$
negative_passages.docid: 50682
negative_passages.text: Prove: $\lim\limits_{n \to \infty} \int_{0}^{\sqrt n}(1-\frac{x^2}{n})^ndx=\int_{0}^{\infty} e^{-x^2}dx$
negative_passages.docid: 104227
negative_passages.text: How to obtain the limit of $xy\log(x^2+y^2)$ when $(x,y)\to(0,0)$ without using polar coordinates or L'Hôpital?
negative_passages.docid: 91023
negative_passages.text: Limit of $y$ if limit of $y+y'$ goes to $0$?
negative_passages.docid: 94466
negative_passages.text: evaluating the limit $ \lim_{(x,y) \rightarrow (0,0) } \frac{x^2y^2}{x^2 + y^2} $
negative_passages.docid: 144633
negative_passages.text: Verification of proof involving logarithms and limits
negative_passages.docid: 157577
negative_passages.text: Prove that $\lim_{x\to y} \frac{d(x, F )}{|x−y|} = 0$ for a.e. $y \in F$.