New posts in Uniform Convergence

Prove $ \lim_{h\rightarrow 0}\frac{1}{h}\int_a^x[f(t+h)-f(t)]\mathrm{d}t=f(x)-f(a). $

$\{f_n\}$ be a sequence of continuous functions converging pointwise to $0$, show $\lim \int_0^1 f_n dx = 0$

If $f(x+1/n)$ converges to a continuous function $f(x)$ uniformly on $\mathbb{R}$, is $f(x)$ necessarily uniformly continuous?

$\frac{1}{2r}\int_{x-r}^{x+r}f(t)dt \to g(x)$ uniformly when $r\rightarrow \infty$, then $g(x)=ax+b$

Show that $\phi(x):=\sum_{n=1}^{\infty}\frac{(-1)^{n}}{\sqrt{n}(1+\frac{x^{2}}{n})^{n}}$ is differentiable on $\mathbb{R}$.

Show that the sequence of functions $\{f_n\}$ is not uniformly convergent on $\Bbb R.$

Can Abel's test and Dirichlet test be used interchangably?

Does $\sum_{n=0}^{\infty} \frac{x^2}{(1+x^2)^n}$ converge uniformly on $(-\infty,\infty)$?

Counterexample around Dini's Theorem

Differentiability of $\sum_{k=0}^{\infty}c_{k}e^{ikt}$ given $\lim_{k\to\infty}k^{m}c_{k}=0$