Question

Prove that $\frac{x}{e^x}$ tends to zero as $x \to \infty $

score 861 · Answer 1 · 2026-03-24 23:45:09

861

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Prove that $\frac{x}{e^x}$ tends to zero as $x \to \infty $

Published on 24 Mar 2026 - 23:45

score 87 · Answer 2 · 2026-03-25 01:17:40

87

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Is there a name for the theorem that $\lim\limits_{n \to \infty} (1+\frac{1}{n})^n < \infty$?

Published on 25 Mar 2026 - 1:17

score 86 · Answer 3 · 2026-03-25 01:18:42

86

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How to find $x$ in $\sum\limits_{i=1}^{\infty}\sum\limits_{j=1}^{\infty}x^{ij}=\frac{1}{1-\gamma}$ if $0\lt x\lt1$?

Published on 25 Mar 2026 - 1:18

score 25 · Answer 4 · 2026-03-24 23:44:37

Help me understand e (exponential/euler's number) and how taking e to a certain power changes time period and return??

score 115 · Answer 5 · 2026-03-24 23:49:55

115

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Can this be correct $\lim_{n\to \infty}\int_0^{\pi\over 2}\cos x\cos\left({x\over n }\right)\ln(\ln\csc x) \, dx = -\gamma?$

Published on 24 Mar 2026 - 23:49

score 233 · Answer 6 · 2026-03-24 23:44:35

233

Views

[[complex]] Solutions of $x=\sqrt{\sin{x}}$

Published on 24 Mar 2026 - 23:44

score 98 · Answer 7 · 2026-03-24 23:43:16

98

Views

Intuitive understanding of some important exponential functions

Published on 24 Mar 2026 - 23:43

score 344 · Answer 8 · 2026-05-10 10:56:53

344

Views

Explicit series for the minimum point of the Gamma function?

Published on 10 May 2026 - 10:56

score 134 · Answer 9 · 2026-03-25 01:18:34

134

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Is $\lim_{x\to \infty}{\sum_{i,h=1}^x \frac{1}{i^h} - x-\ln{x}}$ equal to $\gamma$, the Euler-Mascheroni constant? If so, why?

Published on 25 Mar 2026 - 1:18

score 83 · Answer 10 · 2026-03-24 23:43:20

83

Views

What's the process in rectangular form for deriving $(a+bi)^{a+bi}$?

Published on 24 Mar 2026 - 23:43

score 705 · Answer 11 · 2026-03-25 01:18:46

705

Views

What are the roots of the equation $z^{40} - z^{20} - a(a+1)$?

Published on 25 Mar 2026 - 1:18

score 323 · Answer 12 · 2026-04-01 09:29:55

323

Views

Why does the constant of integration move?

Published on 01 Apr 2026 - 9:29

score 58 · Answer 13 · 2026-03-24 23:42:51

58

Views

Why does the sign flip when substituting in Euler's formula

Published on 24 Mar 2026 - 23:42

score 3.1k · Answer 14 · 2026-03-25 01:15:24

3.1k

Views

Is there another proof for Euler–Mascheroni Constant?

Published on 25 Mar 2026 - 1:15

score 551 · Answer 15 · 2026-03-24 23:48:11

551

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Number of real roots of equation $e^{\cos x} - e^{-\cos x} - 4 = 0$?

Published on 24 Mar 2026 - 23:48

List Question

Prove that $\frac{x}{e^x}$ tends to zero as $x \to \infty $

Is there a name for the theorem that $\lim\limits_{n \to \infty} (1+\frac{1}{n})^n < \infty$?

How to find $x$ in $\sum\limits_{i=1}^{\infty}\sum\limits_{j=1}^{\infty}x^{ij}=\frac{1}{1-\gamma}$ if $0\lt x\lt1$?

Help me understand e (exponential/euler's number) and how taking e to a certain power changes time period and return??

Can this be correct $\lim_{n\to \infty}\int_0^{\pi\over 2}\cos x\cos\left({x\over n }\right)\ln(\ln\csc x) \, dx = -\gamma?$

[[complex]] Solutions of $x=\sqrt{\sin{x}}$

Intuitive understanding of some important exponential functions

Explicit series for the minimum point of the Gamma function?

Is $\lim_{x\to \infty}{\sum_{i,h=1}^x \frac{1}{i^h} - x-\ln{x}}$ equal to $\gamma$, the Euler-Mascheroni constant? If so, why?

What's the process in rectangular form for deriving $(a+bi)^{a+bi}$?

What are the roots of the equation $z^{40} - z^{20} - a(a+1)$?

Why does the constant of integration move?

Why does the sign flip when substituting in Euler's formula

Is there another proof for Euler–Mascheroni Constant?

Number of real roots of equation $e^{\cos x} - e^{-\cos x} - 4 = 0$?

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