Question

Proof of $\limsup_{n\to\infty} x_{kn} \leq \limsup_{n\to\infty} x_{n}$

score 63 · Answer 1 · 2026-04-14 07:45:35

63

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Proof of $\limsup_{n\to\infty} x_{kn} \leq \limsup_{n\to\infty} x_{n}$

Published on 14 Apr 2026 - 7:45

score 141 · Answer 2 · 2026-04-17 14:30:27

141

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Prob. 5 (b), Sec. 4.3, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: Rigorous Proof of a Limit Statement

Published on 17 Apr 2026 - 14:30

score 95 · Answer 3 · 2026-05-06 10:43:08

95

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Find $\;\lim{\frac{f'(x)}{f(x)}}\;$ where $f(x)$ is a solution to differential equation

Published on 06 May 2026 - 10:43

score 104 · Answer 4 · 2026-04-16 22:53:01

104

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Find $\lim_{x\rightarrow 1^{\pm}}\big({\frac {2x+3}{x^2-1}}\big)$

Published on 16 Apr 2026 - 22:53

score 726 · Answer 5 · 2026-04-25 20:52:00

726

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Prob. 5 (e), Sec. 4.3, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: How to find $\lim_{x\to 0-} \frac{\sqrt{x+1}}{x}$?

Published on 25 Apr 2026 - 20:52

score 61 · Answer 6 · 2026-04-11 12:15:55

61

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How do I compute this limit?

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score 599 · Answer 7 · 2026-05-10 19:50:30

599

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score 260 · Answer 8 · 2026-05-10 19:52:09

260

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Show that a holomorphic function $f$ has a pole iff we can find $g$ s.t. $f(z) = \frac{g(z)}{(z-z_0)^m}$

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score 734 · Answer 9 · 2026-04-09 01:56:09

734

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score 70 · Answer 10 · 2026-04-16 11:54:06

70

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score 96 · Answer 11 · 2026-04-12 12:26:50

96

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56

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152

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215

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score 183 · Answer 15 · 2026-04-14 07:37:46

183

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List Question

Proof of $\limsup_{n\to\infty} x_{kn} \leq \limsup_{n\to\infty} x_{n}$

Prob. 5 (b), Sec. 4.3, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: Rigorous Proof of a Limit Statement

Find $\;\lim{\frac{f'(x)}{f(x)}}\;$ where $f(x)$ is a solution to differential equation

Find $\lim_{x\rightarrow 1^{\pm}}\big({\frac {2x+3}{x^2-1}}\big)$

Prob. 5 (e), Sec. 4.3, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: How to find $\lim_{x\to 0-} \frac{\sqrt{x+1}}{x}$?

How do I compute this limit?

$f$ zero (essential singularity) $\implies \frac 1 f$ pole (essential singularity)

Show that a holomorphic function $f$ has a pole iff we can find $g$ s.t. $f(z) = \frac{g(z)}{(z-z_0)^m}$

Complete proof about the limits of a multivariable function

Taylor expansion of $\ln\left(1+\frac1x\right)$

A problem related with limit and continuity.

Calculus: function satisfies limit conditions

A Subtle Point in Rudin's Proof on $e$

Cesaro limits and supremum of a sequence

A question concerning Cesaro-Stolz theorem

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