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Uniform convergence of the derivative function $h_n'(x)$

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Point wise and uniform convergence of sequences of functions

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53
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Uniform convergence of sequence of differentiable functions

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34
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Show that the sequence of derivatives $(h_n')$ diverges for every $x\in\mathbf{R}$, where $h_n(x)=\frac{\sin nx}{\sqrt{n}}$

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142
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Showing that $\lim f_n'=f'$ where $f_n(x)=\frac{nx^2+1}{2n+x}$ and $f = \lim f_n = \frac{x^2}{2}$

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180
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On Bartle's 'Elements of Integration' Exercise 7.U

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103
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Converse of the Weierstrass M-Test

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70
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Interval of convergence of the infinite series $g(x)=\sum_{n=0}^{\infty}\frac{x^{2n}}{1+x^{2n}}$

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62
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Analyzing convergence of sequence of functions

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71
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Interval of convergence of the infinite series $\sum_{n=1}^{\infty} \frac{x^n}{1+x^n}$

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66
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Finding the interval of convergence of the infinite series $\sum_{n=1}^{\infty}\frac{2^n + x^n}{1+3^n x^n}$

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129
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Convergence, continuity and differentiability of $f(x)=\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+2}-\frac{1}{x+3}+\ldots$

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76
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Convergence of a sequence of functions with different domains

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#ordinary-differential-equations #convergence-divergence #sequence-of-function
118
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Exploring the continuous nowhere differentiable function $g(x) = \sum_{n=0}^{\infty} \frac{\cos {2^n x}}{2^n}$

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294
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Is $f(x)=\sum_{k=1}^{\infty} \frac{\sin (x/k)}{k}$ continuous, differentiable and twice-differentiable?

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