Is $f(x,y) = \frac{x^ny^m}{x^{n'}+y^{m'}}$ continuous at origin?
37489
Show that $ \lim_{(x,y) \to 0} \frac {|x|^ \alpha |y|^ \beta} {|x|^ \gamma + |y|^ \delta} \text {exists} \iff \alpha/\gamma + \beta/\delta > 1.$
141945
Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
33499
For which $a\in \mathbb{R}$ is $f(x,y) = \frac{xy^a}{x^2+y^2}$ with $f(0,0)=0$ continuous?
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
63598
Is every separately continuous function on $R^2$ continuous?
50725
Inverse of function is continuous or not?
46642
Continuity of $\sin(x)/x$
87743
Is a function whose derivative vanishes at rationals constant?
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
29180
If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
147516
Continuous function whose right hand derivative equals 0 is constant?
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
150554
proof that $f'$ is continuous at $a$
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
74145
How to prove $x^{n}$ is not uniformly continuous