Find a sequence of differentiable functions $\{f_n\}$ on $[0,1]$ such that $f_n \to 0$ uniformly, but $\{f_n'(1/2)\}$ does not converge to $0$.
127224
Sequence uniform convergence but the derivatives are not.
65312
Check the uniform convergence of series of functions
67791
Can I exchange limit and differentiation for a sequence of smooth functions?
37736
How to find a function in $ L_{2}(0,\infty)$ but not $L_{q}(0,\infty)$, $q\neq 2 $
101701
Prove that $\ln x$ is not uniformly continuous on $(0,1]$
54137
Find a non-negative function on [0,1] such that $t\cdot m(\{x:f(x) \geq t\}) \to 0$ that is not Lebesgue Integrable
76593
Show that $f_n(z)=z^n$ converges locally uniformly on $|z|<1$ but not uniformly(?)
71140
Pointwise limit of the sequence of continuously differentiable functions defined inductively.
125190
Convergence to function that is not measurable
112730
uniform convergence and function $\partial^k f_n(z_n) \rightarrow \partial^k f(z_0)$
153063
Uniform convergence of $f_n(x)=nx^n(1-x)$ for $x \in [0,1]$?
55337
Find a sequence of functions $\{g_n\}$ in $C([0,1])$ so that $\overline{\{g_n\}}$ is compact, but $g_n$ does not converge uniformly.
135450
Prove $x^n$ is not uniformly convergent
88147
Show that $g_n(x)=nf(x+1/n)-nf(x)$ converges uniformly to $f'$
148349
Uniform convergence with two sequences of functions
55826
Convergence of sequence of real numbers and (sub)subsequence
4157
Function Sequence Uniform Convergence