Question

Prove that $ \lim_{x\to 0}\bigg[ \ln \bigg(\frac{1+\cos(x)}{1-\cos(x)} \bigg)\bigg] \sim 2\ln |x|$

score 78 · Answer 1 · 2019-06-10 17:53:41

78

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Prove that $ \lim_{x\to 0}\bigg[ \ln \bigg(\frac{1+\cos(x)}{1-\cos(x)} \bigg)\bigg] \sim 2\ln |x|$

Published on 10 Jun 2019 - 17:53

score 216 · Answer 2 · 2026-03-31 13:44:45

216

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Discrete math: Big O notation proof with logarithms

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score 105 · Answer 3 · 2026-04-02 03:50:11

105

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How to prove that for all non-negative $\forall x\in\mathbb R: x\ge \frac{\ln^2(1+x+\sqrt{2x})}{2}$?

Published on 02 Apr 2026 - 3:50

score 124 · Answer 4 · 2026-03-25 11:25:36

124

Views

Interpolation between iterations of exponentials (and logarithms)

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score 24 · Answer 5 · 2026-04-02 10:08:23

24

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Discrete math - proving big omega concerns about solution

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score 190 · Answer 6 · 2026-03-27 04:58:54

190

Views

How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$?

Published on 27 Mar 2026 - 4:58

score 40 · Answer 7 · 2019-06-13 13:21:31

40

Views

$f(f(x)) = \log(x) \forall x > 0$, what is $f$?

Published on 13 Jun 2019 - 13:21

score 188 · Answer 8 · 2019-06-13 14:32:42

188

Views

$\log_{10}(x)$ approximation

Published on 13 Jun 2019 - 14:32

score 2.1k · Answer 9 · 2026-03-25 01:38:29

2.1k

Views

Defining a holomorphic branch of $f(z)=\log(z^2-1)$

Published on 25 Mar 2026 - 1:38

score 300 · Answer 10 · 2019-06-13 21:38:51

300

Views

logarithmic rules with functions

Published on 13 Jun 2019 - 21:38

score 885 · Answer 11 · 2026-03-25 23:36:22

885

Views

does ln(-1)=0? What did I do wrong in my proof?

Published on 25 Mar 2026 - 23:36

score 72 · Answer 12 · 2019-06-15 16:01:57

72

Views

Why is the function $f$ undefined for $x=1$ when $f(x) = \log_x x$.

Published on 15 Jun 2019 - 16:01

score 307 · Answer 13 · 2026-04-02 06:15:13

307

Views

Proving a function $f$ has a holomorphic logarithm $g$

Published on 02 Apr 2026 - 6:15

score 140 · Answer 14 · 2026-04-02 03:12:08

140

Views

Logarithmic and exponential functions

Published on 02 Apr 2026 - 3:12

score 63 · Answer 15 · 2019-06-16 15:15:19

63

Views

Find $\left\lfloor\prod_{j=3}^{2020}\log_{j-1}j\right\rfloor$.

Published on 16 Jun 2019 - 15:15

List Question

Prove that $ \lim_{x\to 0}\bigg[ \ln \bigg(\frac{1+\cos(x)}{1-\cos(x)} \bigg)\bigg] \sim 2\ln |x|$

Discrete math: Big O notation proof with logarithms

How to prove that for all non-negative $\forall x\in\mathbb R: x\ge \frac{\ln^2(1+x+\sqrt{2x})}{2}$?

Interpolation between iterations of exponentials (and logarithms)

Discrete math - proving big omega concerns about solution

How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$?

$f(f(x)) = \log(x) \forall x > 0$, what is $f$?

$\log_{10}(x)$ approximation

Defining a holomorphic branch of $f(z)=\log(z^2-1)$

logarithmic rules with functions

does ln(-1)=0? What did I do wrong in my proof?

Why is the function $f$ undefined for $x=1$ when $f(x) = \log_x x$.

Proving a function $f$ has a holomorphic logarithm $g$

Logarithmic and exponential functions

Find $\left\lfloor\prod_{j=3}^{2020}\log_{j-1}j\right\rfloor$.

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