Question

How to determine the convergence or divergence of this sequence without resort to the L'Hospital's rule?

score 62 · Answer 1 · 2026-04-14 20:44:24

62

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How to determine the convergence or divergence of this sequence without resort to the L'Hospital's rule?

Published on 14 Apr 2026 - 20:44

score 83 · Answer 2 · 2026-04-15 10:31:40

83

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Proving some statements, given that $|f(x)-f(y)| \leq M|x-y|^{\alpha}$

Published on 15 Apr 2026 - 10:31

score 55 · Answer 3 · 2026-04-16 20:24:40

55

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If $\lim_{x\rightarrow x_{0}}f'(x)=a\in{\mathbb R} $ then $f'(x_{0})=a$

Published on 16 Apr 2026 - 20:24

score 866 · Answer 4 · 2026-04-15 13:50:41

866

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Prove that $\sin(1 + k^3) \not \to 0$

Published on 15 Apr 2026 - 13:50

score 62 · Answer 5 · 2026-04-14 05:05:23

62

Views

How to show that the $\lim_{n \to \infty} x_n$ exists?

Published on 14 Apr 2026 - 5:05

score 52 · Answer 6 · 2026-04-15 12:40:06

52

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Determine the limit by the condition given

Published on 15 Apr 2026 - 12:40

score 446 · Answer 7 · 2026-04-16 20:20:08

446

Views

How to prove a sequence diverges? $a_n^\infty,$ defined by $a_{n+1}=-1-a_n^{2},\qquad a_1=1$

Published on 16 Apr 2026 - 20:20

score 2.1k · Answer 8 · 2026-04-16 20:46:16

2.1k

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Proof check: Prove if $f'$ is periodic, then $f$ is periodic

Published on 16 Apr 2026 - 20:46

score 75 · Answer 9 · 2026-04-16 06:24:29

75

Views

Proving $\lim_\limits{x \to 0} \frac{f(x)}{g(x)} = \frac{\lim_{x \to 0} f(x)}{\lim_{x \to 0} g(x)}$

Published on 16 Apr 2026 - 6:24

score 58 · Answer 10 · 2026-04-07 21:22:25

58

Views

Limit of a function defined as an integral

Published on 07 Apr 2026 - 21:22

score 219 · Answer 11 · 2026-04-16 12:53:43

219

Views

Evaluating the limit ${\lim_\limits{x\to0^+}\frac{e^x-\cos(\lambda \sqrt x)}{\sqrt {1+\sin(\lambda x)}-1}}$

Published on 16 Apr 2026 - 12:53

score 1.4k · Answer 12 · 2026-04-09 11:41:32

1.4k

Views

Proving Rolle's Theorem

Published on 09 Apr 2026 - 11:41

score 115 · Answer 13 · 2026-04-13 19:14:16

115

Views

L'Hôpital evaluating limits for multivariable functions?

Published on 13 Apr 2026 - 19:14

score 137 · Answer 14 · 2026-04-12 18:11:14

137

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Limit of vectors and limit of components

Published on 12 Apr 2026 - 18:11

score 38 · Answer 15 · 2026-04-15 08:52:56

38

Views

Proving the slopes to the left and right of a maximum

Published on 15 Apr 2026 - 8:52

List Question

How to determine the convergence or divergence of this sequence without resort to the L'Hospital's rule?

Proving some statements, given that $|f(x)-f(y)| \leq M|x-y|^{\alpha}$

If $\lim_{x\rightarrow x_{0}}f'(x)=a\in{\mathbb R} $ then $f'(x_{0})=a$

Prove that $\sin(1 + k^3) \not \to 0$

How to show that the $\lim_{n \to \infty} x_n$ exists?

Determine the limit by the condition given

How to prove a sequence diverges? $a_n^\infty,$ defined by $a_{n+1}=-1-a_n^{2},\qquad a_1=1$

Proof check: Prove if $f'$ is periodic, then $f$ is periodic

Proving $\lim_\limits{x \to 0} \frac{f(x)}{g(x)} = \frac{\lim_{x \to 0} f(x)}{\lim_{x \to 0} g(x)}$

Limit of a function defined as an integral

Evaluating the limit ${\lim_\limits{x\to0^+}\frac{e^x-\cos(\lambda \sqrt x)}{\sqrt {1+\sin(\lambda x)}-1}}$

Proving Rolle's Theorem

L'Hôpital evaluating limits for multivariable functions?

Limit of vectors and limit of components

Proving the slopes to the left and right of a maximum

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