Proving that $\frac{2xy}{x^2+y^2}$ is discontinuous?
97553
Continuity of $\frac{2xy}{x^2+y^2}$ at $(0,0)$
127449
Uniform continuous of $f(x,y) = \sin(x^2+y)$
101130
How to determine the limit of $ f(x, y)=\frac{9xy}{x^2 + y^2}$?
2357
Showing $\frac{x^3y}{x^4+y^2}$ is continuous at all points
142513
Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square.
147299
Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
146594
Prove that $\frac{d}{dx}(\tan^{-1}(x))=\frac{1}{1+x^2}dx$
50509
Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
61539
proof for a basis in $L^2$
69066
$\epsilon{\rm -}\delta$ proof of the discontinuity of Dirichlet's function
141423
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$
13510
Multivariable Delta Epsilon Proof $\lim_{(x,y)\to(0,0)}\frac{x^3y^2}{x^4+y^4}$ --- looking for a hint
12488
Show that $\frac{uu_x + vv_x}{u^2 + v^2}$ is harmonic.
115077
Prove continuity for cubic root using epsilon-delta
135449
Prove: $\frac1x$ is not a uniformly continuous function
91786
Proving and disproving $\exists b,c\in \mathbb R$ such that $f(x)=\frac a2x^2+bx+c $
7358
For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous.