query: Not continuity of a multivariable function given by $\frac{2x^2y}{x^2+y^2}$
positive_passages.docid: 26602
positive_passages.text: Continuity and existence of directional derivatives at all directions of a $f:\mathbb{R}^{2} \to \mathbb{R}$ given by $f(x,y)=\frac{2x^2y}{x^2+y^2}$
negative_passages.docid: 70617
negative_passages.text: Continuity at a point of characteristic function iff the point is not boundary point
negative_passages.docid: 88240
negative_passages.text: Two functions discontinuous, but sum continuous
negative_passages.docid: 3518
negative_passages.text: Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
negative_passages.docid: 9924
negative_passages.text: Derivative of conjugate multivariate function
negative_passages.docid: 57014
negative_passages.text: Existence of a power series converging non-uniformly to a continuous function
negative_passages.docid: 17223
negative_passages.text: Continuity of an inverse function.
negative_passages.docid: 94244
negative_passages.text: $\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$
negative_passages.docid: 30036
negative_passages.text: Function in $H^1$, but not continuous
negative_passages.docid: 64619
negative_passages.text: Continuity of a function of product spaces
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: 85092
negative_passages.text: Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
negative_passages.docid: 117419
negative_passages.text: Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?
negative_passages.docid: 18222
negative_passages.text: Set of continuity points of a real function
negative_passages.docid: 769
negative_passages.text: Find multivariable limit $\frac{x^2y}{x^2+y^3}$
negative_passages.docid: 62606
negative_passages.text: Non-existence of $\lim \limits_{(x, y) \to (0,0)} \frac{x^3 + y^3}{x - y} $
negative_passages.docid: 2129
negative_passages.text: Showing that the derivative operator is not bounded on $L^2 (\mathbb{R})$