Question

Find $\lim \limits_{x\to 0}\frac{\log\left(\cos x\right)}{x^2}$ without L'Hopital

score 950 · Answer 1 · 2026-04-17 02:55:04

950

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Find $\lim \limits_{x\to 0}\frac{\log\left(\cos x\right)}{x^2}$ without L'Hopital

Published on 17 Apr 2026 - 2:55

score 188 · Answer 2 · 2026-04-29 01:00:44

188

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Algebra problem regarding system of logarithmic equations.

Published on 29 Apr 2026 - 1:00

score 37 · Answer 3 · 2026-04-15 05:43:14

37

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Limit of $n^{A\lg n}\cdot 2^{n-n^A}$ for $A > 1$

Published on 15 Apr 2026 - 5:43

score 836 · Answer 4 · 2026-04-15 22:24:32

836

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If $f(x) = ax +b$, is $\ln{f(x)} \equiv \ln(ax+b)$ or $\ln{ax}+\ln{b}$?

Published on 15 Apr 2026 - 22:24

score 336 · Answer 5 · 2026-04-12 21:46:08

336

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Why is $1^{\infty}$ undefined when the limit of it is $\operatorname e$?

Published on 12 Apr 2026 - 21:46

score 148 · Answer 6 · 2026-04-16 12:15:28

148

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Prove that $\ln(x+\sqrt{x^2 + 4}) - \ln2$ is odd

Published on 16 Apr 2026 - 12:15

score 7.3k · Answer 7 · 2026-04-16 02:18:35

7.3k

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How to prove $\lim\limits_{x\to 0}x^m (\ln x)^n = 0$

Published on 16 Apr 2026 - 2:18

score 92 · Answer 8 · 2026-04-13 01:10:34

92

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Prove inequality with logarithms

Published on 13 Apr 2026 - 1:10

score 316 · Answer 9 · 2026-04-16 13:53:05

316

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How to show $\lim_{x\to\infty} \frac{5^{x} - 4^{x}}{3^{x} - 2^{x}} = \infty$

Published on 16 Apr 2026 - 13:53

score 55 · Answer 10 · 2026-04-13 08:08:51

55

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Interpretation of $\log(x)$ for $x$ on $(0,1)$

Published on 13 Apr 2026 - 8:08

score 74 · Answer 11 · 2026-04-15 00:09:01

74

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How do I prove $\lim\limits_{a \to \infty} \ln((\frac{a+n}{a})^a) = n$

Published on 15 Apr 2026 - 0:09

score 10.8k · Answer 12 · 2026-04-14 18:15:25

10.8k

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The sum of series with natural logarithm: $\sum_{n=1}^\infty \ln\left(\frac{n(n+2)}{(n+1)^2}\right)$

Published on 14 Apr 2026 - 18:15

score 3.3k · Answer 13 · 2026-04-15 21:50:14

3.3k

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solve $\log m = \log n + 3/2 \log (1 + v/m^2)$ for m

Published on 15 Apr 2026 - 21:50

score 494 · Answer 14 · 2026-04-17 08:31:29

494

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How can I show $\limsup_n\frac{1}{n}\log(a_n+b_n)=\max\{\limsup_n\frac{1}{n}\log(a_n),\limsup_n\frac{1}{n}\log(b_n)\}$?

Published on 17 Apr 2026 - 8:31

score 1.2k · Answer 15 · 2026-04-14 20:50:26

1.2k

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How to solve $8n^2=64n\cdot \log_2(n)$?

Published on 14 Apr 2026 - 20:50

List Question

Find $\lim \limits_{x\to 0}\frac{\log\left(\cos x\right)}{x^2}$ without L'Hopital

Algebra problem regarding system of logarithmic equations.

Limit of $n^{A\lg n}\cdot 2^{n-n^A}$ for $A > 1$

If $f(x) = ax +b$, is $\ln{f(x)} \equiv \ln(ax+b)$ or $\ln{ax}+\ln{b}$?

Why is $1^{\infty}$ undefined when the limit of it is $\operatorname e$?

Prove that $\ln(x+\sqrt{x^2 + 4}) - \ln2$ is odd

How to prove $\lim\limits_{x\to 0}x^m (\ln x)^n = 0$

Prove inequality with logarithms

How to show $\lim_{x\to\infty} \frac{5^{x} - 4^{x}}{3^{x} - 2^{x}} = \infty$

Interpretation of $\log(x)$ for $x$ on $(0,1)$

How do I prove $\lim\limits_{a \to \infty} \ln((\frac{a+n}{a})^a) = n$

The sum of series with natural logarithm: $\sum_{n=1}^\infty \ln\left(\frac{n(n+2)}{(n+1)^2}\right)$

solve $\log m = \log n + 3/2 \log (1 + v/m^2)$ for m

How can I show $\limsup_n\frac{1}{n}\log(a_n+b_n)=\max\{\limsup_n\frac{1}{n}\log(a_n),\limsup_n\frac{1}{n}\log(b_n)\}$?

How to solve $8n^2=64n\cdot \log_2(n)$?

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