$f_n,f_n^{\prime}\rightarrow 0$ pointwise. But $(f_n^{\prime}) $ is not uniformly convergent. Find an example of such a sequence of functions.
119348
Find sequence of differentiable functions $f_n$ on $\mathbb{R}$ that converge uniformly, but $f'_n$ converges only pointwise
35514
If $\{f_n\}$ converges uniformly and each $f_n$ is bounded, show that $\exists M>0$ s.t. $|f_n(x)| \leq M$
88441
Whether the sequence $\{x_n-y_n\}$ converge or not.
8715
Let $(a_n)_n$ be a convergent sequence of integers , what can we say about $(a_n)_n$
88261
Convergence of a sequence in two different $L_p$ spaces
40797
$(a_n+a_{n+1})$ is convergent implies $(a_n/n)$ converges to $0$
60282
Prove that $f_n$ converges uniformly on $\mathbb{R}$
125190
Convergence to function that is not measurable
155695
The convergence of a sequence
140445
Sequence of continuous functions whose pointwise limit is discontinuous
92734
Existence of a sequence of continuous functions convergent pointwise to the indicator function of irrational numbers
4157
Function Sequence Uniform Convergence
140901
Uniform convergence of $f_n(z)=nz^n$ in the set $|z|<\frac{1}{2}$
107619
Suppose $\sum a_n$ converges absolutely and $\sum b_n$ converges. Give an example where the Cauchy product does not converge absolutely.
157762
Showing $f_n(x):=\frac{x}{1+n^2x^2}$ uniformly convergent in $\mathbb R$ using $\epsilon-n_0$
25532
Determine if the convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ is uniform.
98762
$f_n(x) = x - x^n$ for $x\in [0,1]$. Does the sequence converge pointwise or uniformly on $[0,1]$?