How to prove the continuity of the function of several at $(0,0)$
129011
Is there limit $ \lim_{(x,y) \to (0,0)} \frac{x^3}{x^2 + y^2}$?
104263
How to show that $f'(x)<2f(x)$
53349
Prove that $\sqrt{x}$ is continuous on its domain $[0, \infty).$
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
40297
Proof of uniform limit of Continuous Functions
12349
a construction of a continuous function from a normal space to [0,1]
81223
Real Analysis Question: continuity of $f(x) = \sum_{q_n<x} 1/n^2$
74950
Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$
46834
show that a distance function is continuous
11017
Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?
14896
Prove: the set of zeros of a continuous function is closed.
8836
If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
115077
Prove continuity for cubic root using epsilon-delta
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
57023
If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$