show that $ f $ is continuous in $a$
135999
One sided limit of an increasing function defined on an open interval
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
16212
If $f$ is continuous, nonnegative on $[a, b]$, show that $\int_{a}^{b} f(x) d(x) = 0$ iff $f(x) = 0$
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
29154
$f$ is continuous and open implies $f$ injective
12523
Supremum of a Continuous Function is Continuous
104263
How to show that $f'(x)<2f(x)$
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
129073
If $f'$ is bounded, then $f$ is uniformly continuous
122585
Show that a function almost everywhere continuous is measurable
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
138105
Let $f$ and $g$ be continuous at $ x=a$, with $f(a)<g(a)$. Prove that there exists a neighborhood $I$ of a such that $f(x)<g(x)$ for all $x \in I$.
28399
Showing $f$ is constant
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
100187
Show function is continuous at origin