Question

Finding $\lim\limits_{x\to0+} (\frac{e^x-1}{x})^{\frac1x}$ without Taylor's series.

score 111 · Answer 1 · 2026-04-17 10:33:24

111

Views

Finding $\lim\limits_{x\to0+} (\frac{e^x-1}{x})^{\frac1x}$ without Taylor's series.

Published on 17 Apr 2026 - 10:33

score 506 · Answer 2 · 2026-04-26 03:22:36

506

Views

Does the function $f(x) = |x|e^x$ have a derivative at $x = 0$?

Published on 26 Apr 2026 - 3:22

score 51 · Answer 3 · 2026-04-29 15:27:57

51

Views

For $f:[-1,1]\longrightarrow \mathbb{R}, f(x) =\arcsin(1-2x^2)$. Check if $f$ is differentiable at $\boldsymbol{x = 0}$

Published on 29 Apr 2026 - 15:27

score 35 · Answer 4 · 2026-04-16 10:07:32

35

Views

Correct reasoning for continuity of $f$ in $(0,0,0)$

Published on 16 Apr 2026 - 10:07

score 99 · Answer 5 · 2026-04-16 15:27:12

99

Views

Limit $\lim_{n\to\infty} n^2\left(\sqrt{1+\frac{1}{n}}+\sqrt{1-\frac{1}{n}}-2\right)$

Published on 16 Apr 2026 - 15:27

score 131 · Answer 6 · 2026-04-15 09:26:03

131

Views

Is $\int_{\infty}^{\infty^2} f(t) dt$ always $0$?

Published on 15 Apr 2026 - 9:26

score 53 · Answer 7 · 2026-05-14 05:00:21

53

Views

Limit of sequences with the squeeze theorem with sequences

Published on 14 May 2026 - 5:00

score 59 · Answer 8 · 2026-04-14 16:37:02

59

Views

$\lim_{x \to 1} \dfrac{\ln(x^2+1)-\ln(2)}{x-1} $ = 1, why?

Published on 14 Apr 2026 - 16:37

score 68 · Answer 9 · 2026-05-14 05:17:30

68

Views

What can we say about the series $\sum_{n=1}^{\infty}n\cdot (1-\cos(\frac{a}{n}))$

Published on 14 May 2026 - 5:17

score 350 · Answer 10 · 2026-05-10 17:57:07

350

Views

What is the correct proof that when $\epsilon$ decreases (in a limit) then the largest $\delta$ should also decrease?

Published on 10 May 2026 - 17:57

score 244 · Answer 11 · 2026-04-15 07:15:52

244

Views

How to prove that $x\ln\left(\frac{e^x+1}{e^x-1}\right)$ tends to $0$ as $x\to0,\infty$

Published on 15 Apr 2026 - 7:15

score 94 · Answer 12 · 2026-04-15 11:23:38

94

Views

Find the constant $p$ and $q$ in the $\lim_{x \to \infty}$

Published on 15 Apr 2026 - 11:23

score 182 · Answer 13 · 2026-05-10 16:55:37

182

Views

Nonsmooth initial data in the conservation laws, their approximations and limits

Published on 10 May 2026 - 16:55

score 133 · Answer 14 · 2026-04-15 07:30:16

133

Views

Why $\lim_{x \to \infty}\int_x^{x+1}\ e^{t^2} \, dt=\infty$?

Published on 15 Apr 2026 - 7:30

score 61 · Answer 15 · 2026-04-29 16:15:55

61

Views

some limiting information about a function from it's first and second derivative

Published on 29 Apr 2026 - 16:15

List Question

Finding $\lim\limits_{x\to0+} (\frac{e^x-1}{x})^{\frac1x}$ without Taylor's series.

Does the function $f(x) = |x|e^x$ have a derivative at $x = 0$?

For $f:[-1,1]\longrightarrow \mathbb{R}, f(x) =\arcsin(1-2x^2)$. Check if $f$ is differentiable at $\boldsymbol{x = 0}$

Correct reasoning for continuity of $f$ in $(0,0,0)$

Limit $\lim_{n\to\infty} n^2\left(\sqrt{1+\frac{1}{n}}+\sqrt{1-\frac{1}{n}}-2\right)$

Is $\int_{\infty}^{\infty^2} f(t) dt$ always $0$?

Limit of sequences with the squeeze theorem with sequences

$\lim_{x \to 1} \dfrac{\ln(x^2+1)-\ln(2)}{x-1} $ = 1, why?

What can we say about the series $\sum_{n=1}^{\infty}n\cdot (1-\cos(\frac{a}{n}))$

What is the correct proof that when $\epsilon$ decreases (in a limit) then the largest $\delta$ should also decrease?

How to prove that $x\ln\left(\frac{e^x+1}{e^x-1}\right)$ tends to $0$ as $x\to0,\infty$

Find the constant $p$ and $q$ in the $\lim_{x \to \infty}$

Nonsmooth initial data in the conservation laws, their approximations and limits

Why $\lim_{x \to \infty}\int_x^{x+1}\ e^{t^2} \, dt=\infty$?

some limiting information about a function from it's first and second derivative

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