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What is the proof behind $\lim f(g(x)) = f(\lim g(x))$?

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#calculus #limits #continuity #epsilon-delta
318
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Find the radius of convergence of the series $\sum a_n z^n$ when: $a_n = \frac{(n!)^3}{(3n)!}$.

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#sequences-and-series #analysis #limits #limsup-and-liminf
45
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Why do we only compute the limit of a function at a point in a CLOSED set?

Published on
#calculus #general-topology #limits
99
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Is my proof correct for scaling of limits?

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#calculus #limits #proof-verification #epsilon-delta
78
Views

Is my proof correct for summing of limits?

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#calculus #limits #proof-verification #epsilon-delta
469
Views

Is my limit quotient proof correct?

Published on
#calculus #limits #proof-verification #epsilon-delta
486
Views

Combinatorial Limit

Published on
#calculus #combinatorics #limits #binomial-coefficients
39
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Finding the limit of expression used for the central limit theorem

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#probability #limits #probability-theory #central-limit-theorem #probability-limit-theorems
74
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Find the limit of $\frac{e^n}{2^n+1}$ as $n→\infty$

Published on
#real-analysis #sequences-and-series #limits #limits-without-lhopital
81
Views

Help me to find the second limit

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#calculus #real-analysis #sequences-and-series #limits
43
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$\lim_{n \rightarrow \infty}\bigcup\limits_{k \ge n} A_k$ of $A_n:=$ open circle with radius $=1 $ and center $(\frac{(-1)^n}{n}, 0)$

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#calculus #linear-algebra #geometry #analysis #limits
356
Views

Prove that the recursive sequence $(a_n)_{n \ge 1}$ is convergent and find its limit

Published on
#real-analysis #sequences-and-series #limits #convergence-divergence
69
Views

Is my product proof for limits correct?

Published on
#calculus #limits #proof-verification #epsilon-delta
57
Views

how to find the value of the $k$ to make $\lim_{x\to 0} \frac{\sqrt[5]{x+\sqrt[3]{x}}-\sqrt[3]{x+\sqrt[5]{x}}}{x^{k}}=A$ exist?

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#limits
58
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Prove that the sequence $\ y_n= \frac{1}{x_1-2}+ \frac{1}{x_2-2}+...+\frac{1}{x_n-2}$ converges and find it`s limit

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#calculus #real-analysis #limits

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