query: Suppose that $f_k$ is a sequence of differentiable functions that converges uniformly to a function $f$. Must $f$ be differentiable?
positive_passages.docid: 143593
positive_passages.text: A sequence of differentiable functions that converge uniformly to a non differentiable function - is my example correct?
negative_passages.docid: 124382
negative_passages.text: Showing that $f_n:[0,1]\to\mathbb{R}$ when $f_n=nx(1-x)^n$ converges pointwise but not uniformly
negative_passages.docid: 37850
negative_passages.text: Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
negative_passages.docid: 88147
negative_passages.text: Show that $g_n(x)=nf(x+1/n)-nf(x)$ converges uniformly to $f'$
negative_passages.docid: 154881
negative_passages.text: Question on differentiability of a continuous function
negative_passages.docid: 65312
negative_passages.text: Check the uniform convergence of series of functions
negative_passages.docid: 127224
negative_passages.text: Sequence uniform convergence but the derivatives are not.
negative_passages.docid: 65474
negative_passages.text: Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence
negative_passages.docid: 127251
negative_passages.text: $f_n(x) = \cos \left( \sqrt{x^2 + \frac{1}{n} }\right)$ is uniformly convergent
negative_passages.docid: 129324
negative_passages.text: Let $f:[0;1]\to\mathbb R$ be continiously differentiable
negative_passages.docid: 144957
negative_passages.text: Uniform convergence of a function
negative_passages.docid: 66758
negative_passages.text: $f_n:[0,1]\to [0,1]$ continuous, $f_n\to f$ uniformly, prove: ${\frac1n}\sum_{k=1}^{n}{f_k} \to f$ uniformly
negative_passages.docid: 155695
negative_passages.text: The convergence of a sequence
negative_passages.docid: 41482
negative_passages.text: $f_n → f$ uniformly on $S$ and each $f_n$ is cont on $S$. Let $(x_n)$ be a sequence of points in $S$ converging to $x \in S$. Then $f_n(x_n) → f(x)$.
negative_passages.docid: 78751
negative_passages.text: holomorphic functions uniformly convergent on any compact subset of an open set implies uniformly convergent on the whole open set.
negative_passages.docid: 144530
negative_passages.text: is uniform convergent sequence leads to bounded function?
negative_passages.docid: 102076
negative_passages.text: Sequence of monotone functions converging to a continuous limit, is the convergence uniform?