Continuity of two variable function $\tan^{-1}(y/x)$
39057
Check the differentiablity of $\theta :\mathbb R^2 \setminus\{(0,0)\}\to \mathbb R$
85623
Proof of continuity implied by differentiability
12349
a construction of a continuous function from a normal space to [0,1]
34940
Continuity of $f(x) = x^n$
2506
twice differentiable functions
147299
Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
125682
Proof verification: the product of two continuous functions is continuous
125745
continuity of power series
88240
Two functions discontinuous, but sum continuous
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
82210
Analytic continuation of function continuous on boundary
98363
Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$
126212
Proving uniform continuity on an interval
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
98772
Continuity of a function in $\mathbb{R}$
11017
Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?