Prove the absolute value function of a continuous function is continuous
44574
Continuity of absolute value of a function
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
62887
Proof that a linear transformation is continuous
44607
Prove that a continuous function on a closed interval attains a maximum
62270
Given two increasing continuous functions $f,g$ prove that $(b-a) \int^b_a f(x)g(x) dx > \int^b_a f(x) dx \int^b_a g(x) dx$
31548
Proof of "every convex function is continuous"
15914
Prove that any polynomial function is continuous
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
13852
Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone
158888
Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$.
132478
Prove that continuous functions mapping irrationals to rationals must be constant
28730
product of two uniformly continuous functions is uniformly continuous
126632
Proving Inequalities with Absolute values
34836
Composition of Absolutely Continuous Functions
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
139763
A function takes every function value twice - proof it is not continuous
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous