Continuity of $f$ and the existence of $f'(x)$ given $\lim_{x\rightarrow 0} f'(x)$ exists.
133405
$\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists?
134752
Proof (epsilon delta) for the continuity of a function at a point
6620
If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L<\infty$, does $\lim\limits_{x\rightarrow\infty} f(x) $ exist?
65346
Characterisation of uniformly continuous function
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
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Proof of continuity $f(x+y) = f(x) + f(y)$
15284
$f$ defined on $[1,\infty )$ is uniformly continuous. Then $\exists M>0$ s.t. $\frac{|f(x)|}{x}\le M$ for $x\ge 1$.
26373
Uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ for $x \neq 0$ and $f(0) = 0.$
55125
Continuous right derivative implies differentiability
9614
How does the existence of a limit imply that a function is uniformly continuous
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property of continuous function
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
100979
Uniform continuity of a function and cauchy sequences
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$f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.