how to prove that given f(x) and g(x) is continuous then $f*g(x)$ is also continuous
118207
Prove that the product of two continuous functions is continuous
104369
If $f$ continuous and $f(x^2) = f(x)$, then $f$ is a const
57180
Techniques to prove a function is uniformly continuous
96450
If $f(x)$ is continuous and differentiable function , prove that $f(x) \geq e^{3x}, \forall x \geq 0$
130299
Prove that if a function $f: X\to Y$ continuous then its graph is closed
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
158423
How to prove that if $f$ is continuous a.e., then it is measurable.
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
53627
Proving continuity of $f$
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
12523
Supremum of a Continuous Function is Continuous
26424
If $f(x)<g(x)$ prove that $\lim f(x)<\lim g(x)$
100740
proof of that a continuous function has a fixed point
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
69122
If $f,g$ are uniformly continuous prove $f+g$ is uniformly continuous but $fg$ and $\dfrac{f}{g}$ are not