Showing that the function $f:\mathbb R^2\to\mathbb R$ is continuous
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
23617
Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
72044
prove $x \mapsto x^2$ is continuous
87239
Prove functions defined by sup and inf are continuous
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
86472
$f:\mathbb R \to \mathbb R^n$ be such that $G(f):=\{(x,f(x)):x \in \mathbb R\}$ is closed and connected in $\mathbb R^{n+1}$ , is $f$ continuous ?
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
75479
Proving that this function is continuous on $G\times G$
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
15579
Show that $f$ is uniformly continuous if limit exists
17223
Continuity of an inverse function.
53627
Proving continuity of $f$
93461
Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.