query: Is this proof of the $\lim_{(x,y)\to (0,0))} \frac{x^6y}{x^8+y^4}$ correct?
positive_passages.docid: 22598
positive_passages.text: When does the limit $\lim_{(x,y)\to(0,0)} \frac{x^ky^l}{x^{2p}+y^{2q}}$ exist?
negative_passages.docid: 141937
negative_passages.text: Prove that the $\lim_{(x,y) \to (0,0)}h(x,y)$ Does not Exist using Polar Coordinates
negative_passages.docid: 121217
negative_passages.text: How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$?
negative_passages.docid: 9781
negative_passages.text: How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
negative_passages.docid: 5157
negative_passages.text: How to evaluate $ \lim_{(x,y)\to(0,0)}\frac{y^2\sin^2x}{x^4+y^4} $
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: 30181
negative_passages.text: Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
negative_passages.docid: 48935
negative_passages.text: Showing $\lim_{(x,y) \to (0,0)} xy \log(x^2+y^2) = 0$
negative_passages.docid: 144633
negative_passages.text: Verification of proof involving logarithms and limits
negative_passages.docid: 147299
negative_passages.text: Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
negative_passages.docid: 146640
negative_passages.text: Computing $\lim_{(x,y)\to (0,0)}\frac{x+y}{\sqrt{x^2+y^2}}$
negative_passages.docid: 18079
negative_passages.text: Evaluating $\lim\limits_{x\to \infty}\sqrt[6]{x^{6}+x^{5}}-\sqrt[6]{x^{6}-x^{5}}$
negative_passages.docid: 13510
negative_passages.text: Multivariable Delta Epsilon Proof $\lim_{(x,y)\to(0,0)}\frac{x^3y^2}{x^4+y^4}$ --- looking for a hint
negative_passages.docid: 119106
negative_passages.text: Compute: $\lim_{x\to 0}\frac{\sqrt[m]{\cos(\alpha x)}-\sqrt[n]{\cos{(\beta x)}}}{x^2},\;m,n\in\mathbb N,\alpha,\beta\in\mathbb R$
negative_passages.docid: 157577
negative_passages.text: Prove that $\lim_{x\to y} \frac{d(x, F )}{|x−y|} = 0$ for a.e. $y \in F$.
negative_passages.docid: 156011
negative_passages.text: Evaluate $\lim_{y\to 0} \dfrac {(x+y)\sec (x+y) - x\sec x}{y}$
negative_passages.docid: 78921
negative_passages.text: Multivariable limit $\lim_{(x,y)\to (0,0)} \frac {x^2 + y^2}{\sqrt{x^2 +y^2 + 1} - 1}$