Prove that this continuous function?
68818
$\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
22303
How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
86327
If the absolute value of a function is continuous, is the function continuous?
23845
How to prove the continuity of the metric function?
151410
Inequality of continuous functions
104044
Prove continuous functions $f$ and $g$ are equal
120947
continuous real-valued function
124499
Where is the error in my proof that all derivatives are continuous?
53627
Proving continuity of $f$
154034
Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
82001
How to prove the function is a constant
76607
Show that exists a continuous function in $E$ that is not bounded
150447
Prove a differentiable function between banach spaces is continuous
81223
Real Analysis Question: continuity of $f(x) = \sum_{q_n<x} 1/n^2$