Question

Calculate the limit $\lim_{x\to0^+}\frac{\sqrt{\cos(2x)}-\sqrt{1+x\sin(x)}}{\tan^2\frac x2}$

score 102 · Answer 1 · 2026-04-23 11:28:49

102

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Calculate the limit $\lim_{x\to0^+}\frac{\sqrt{\cos(2x)}-\sqrt{1+x\sin(x)}}{\tan^2\frac x2}$

Published on 23 Apr 2026 - 11:28

score 84 · Answer 2 · 2026-04-12 01:11:13

84

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Given a limit value, prove that a given series is absolutely convergent

Published on 12 Apr 2026 - 1:11

score 44 · Answer 3 · 2026-04-13 12:26:06

44

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Limit of expression involving integral and sequence

Published on 13 Apr 2026 - 12:26

score 64 · Answer 4 · 2026-04-14 02:56:28

64

Views

Show that the series converges for all $0 < a < 3$

Published on 14 Apr 2026 - 2:56

score 114 · Answer 5 · 2026-04-16 00:15:53

Simple approaches to prove that $\lim\limits_{x\to 0}\left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)=-\frac13\ $?

score 57 · Answer 6 · 2026-04-15 20:24:31

57

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Calculate the limit of $\left(\frac{n+1}{n-5}\right)^{5n-2}$

Published on 15 Apr 2026 - 20:24

score 85 · Answer 7 · 2026-04-16 01:26:08

85

Views

Find value of $a$ and $b$

Published on 16 Apr 2026 - 1:26

score 111 · Answer 8 · 2026-04-10 01:09:19

111

Views

How to calculate $\pi$

Published on 10 Apr 2026 - 1:09

score 32 · Answer 9 · 2026-04-16 02:28:32

32

Views

If $f:\mathbb R \rightarrow \mathbb R$ is differentiable at $v$, why is $ x\rightarrow f(x-3)$ differentiable at $v+3$?

Published on 16 Apr 2026 - 2:28

score 133 · Answer 10 · 2026-04-15 20:29:54

133

Views

Verify that $\lim_{h\to0} (1+hx)^{1/h} = e^x$

Published on 15 Apr 2026 - 20:29

score 144 · Answer 11 · 2026-04-16 14:04:33

144

Views

Proof Verification: Show that $\lim_{x \to c} x^3 =c^3 $ for any $c \in \mathbb{R}$

Published on 16 Apr 2026 - 14:04

score 53 · Answer 12 · 2026-04-13 08:17:17

53

Views

Cannot find limit

Published on 13 Apr 2026 - 8:17

score 1.3k · Answer 13 · 2026-04-12 00:02:45

1.3k

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Proof Verification: $\lim_{x \to 0} \cos(1/x) $ does not converge

Published on 12 Apr 2026 - 0:02

score 109 · Answer 14 · 2026-04-16 18:03:46

109

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Calculate the following limit: $\lim_{n\to \infty} a_n = \frac{1}{n^5}(1^4 +2^4+....+n^4)$

Published on 16 Apr 2026 - 18:03

score 209 · Answer 15 · 2026-04-18 18:04:38

209

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Double limit in the proof of differentiability

Published on 18 Apr 2026 - 18:04

List Question

Calculate the limit $\lim_{x\to0^+}\frac{\sqrt{\cos(2x)}-\sqrt{1+x\sin(x)}}{\tan^2\frac x2}$

Given a limit value, prove that a given series is absolutely convergent

Limit of expression involving integral and sequence

Show that the series converges for all $0 < a < 3$

Simple approaches to prove that $\lim\limits_{x\to 0}\left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)=-\frac13\ $?

Calculate the limit of $\left(\frac{n+1}{n-5}\right)^{5n-2}$

Find value of $a$ and $b$

How to calculate $\pi$

If $f:\mathbb R \rightarrow \mathbb R$ is differentiable at $v$, why is $ x\rightarrow f(x-3)$ differentiable at $v+3$?

Verify that $\lim_{h\to0} (1+hx)^{1/h} = e^x$

Proof Verification: Show that $\lim_{x \to c} x^3 =c^3 $ for any $c \in \mathbb{R}$

Cannot find limit

Proof Verification: $\lim_{x \to 0} \cos(1/x) $ does not converge

Calculate the following limit: $\lim_{n\to \infty} a_n = \frac{1}{n^5}(1^4 +2^4+....+n^4)$

Double limit in the proof of differentiability

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