How to prove $f(x,y)$ is continuos in $\left(x_{0},y_{0}\right)$?
135113
Is there a step by step checklist to check if a multivariable limit exists and find its value?
11017
Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?
124499
Where is the error in my proof that all derivatives are continuous?
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
13249
Multivariable limit proof: $\lim\limits_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$
15914
Prove that any polynomial function is continuous
85623
Proof of continuity implied by differentiability
31548
Proof of "every convex function is continuous"
87239
Prove functions defined by sup and inf are continuous
23845
How to prove the continuity of the metric function?
66391
Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
105700
Proving $\,f$ is constant.
121771
Proof $f(x)\equiv 0$
104044
Prove continuous functions $f$ and $g$ are equal
104369
If $f$ continuous and $f(x^2) = f(x)$, then $f$ is a const