Question

Lim $x^{(x^x)}$ as $x$ approaches zero from the right

score 110 · Answer 1 · 2026-04-15 16:52:31

110

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Lim $x^{(x^x)}$ as $x$ approaches zero from the right

Published on 15 Apr 2026 - 16:52

score 311 · Answer 2 · 2026-04-16 21:34:43

311

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If $a_1 = 3$ and $a_{n+1}=a_n^2-2$, then $\frac{1}{a_1}+\frac{1}{a_1a_2}+\frac{1}{a_1 a_2 a_3}+\cdots = \frac{3-\sqrt{5}}{2}$

Published on 16 Apr 2026 - 21:34

score 198 · Answer 3 · 2026-04-17 07:31:21

198

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Asymptotics of the sequence defined by $x_{n+1} = x_n + \frac{2}{x_n}$, $x_0=1$

Published on 17 Apr 2026 - 7:31

score 1.5k · Answer 4 · 2026-04-12 13:16:56

1.5k

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Prove that the product of a constant and a continuous function is continuous.

Published on 12 Apr 2026 - 13:16

score 38 · Answer 5 · 2026-04-15 09:11:38

38

Views

If the limit of the sum exists, then the limit of each component exists

Published on 15 Apr 2026 - 9:11

score 96 · Answer 6 · 2026-04-17 04:16:52

96

Views

$\lim_{n\rightarrow \infty} (a_n+b_n)=0$ $\lim_{n\rightarrow \infty} (b_n-c_n)=0$ imply $\lim_{n\rightarrow \infty} (a_n+c_n)=0$?

Published on 17 Apr 2026 - 4:16

score 208 · Answer 7 · 2026-04-16 04:00:52

$\lim_{n\rightarrow \infty} (a_n+b_n)=0$ and $\lim_{n\rightarrow \infty} c_n=L$ imply $\lim_{n\rightarrow \infty} \exp(a_n)*c_n-L*\exp(-b_n)=0$

score 62 · Answer 8 · 2026-04-15 18:24:08

62

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$\lim_{n\rightarrow \infty} (a_n-b_n)=0$ and $\lim_{n\rightarrow \infty} b_n=0$ imply $\lim_{n\rightarrow \infty}a_n=0$?

Published on 15 Apr 2026 - 18:24

score 37 · Answer 9 · 2026-04-15 03:16:29

37

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Compute $ \lim_{n\rightarrow \infty}\frac{\exp(x_j)}{n+\sum_{k=1}^n \exp(x_k)} $ with $x_k$ uniformly bounded

Published on 15 Apr 2026 - 3:16

score 2.4k · Answer 10 · 2026-04-13 22:43:47

2.4k

Views

When to use L'Hospital's rule vs the limit shortcut

Published on 13 Apr 2026 - 22:43

score 51 · Answer 11 · 2026-04-13 17:03:34

51

Views

Finding integers and the limit of a sequence - from a 100 sequence and more (Russian book)

Published on 13 Apr 2026 - 17:03

score 307 · Answer 12 · 2026-04-13 03:47:52

307

Views

How is this proof for the scalar product rule of limits valid?

Published on 13 Apr 2026 - 3:47

score 270 · Answer 13 · 2026-04-17 05:14:33

270

Views

Calculating upper and lower limits for a linear function

Published on 17 Apr 2026 - 5:14

score 58 · Answer 14 · 2026-04-11 00:06:37

58

Views

Does $(1-e^{-y})^n $ converge as $n \to \infty$?

Published on 11 Apr 2026 - 0:06

score 139 · Answer 15 · 2026-04-16 08:42:33

139

Views

Prove that the following sequence converges

Published on 16 Apr 2026 - 8:42

List Question

Lim $x^{(x^x)}$ as $x$ approaches zero from the right

If $a_1 = 3$ and $a_{n+1}=a_n^2-2$, then $\frac{1}{a_1}+\frac{1}{a_1a_2}+\frac{1}{a_1 a_2 a_3}+\cdots = \frac{3-\sqrt{5}}{2}$

Asymptotics of the sequence defined by $x_{n+1} = x_n + \frac{2}{x_n}$, $x_0=1$

Prove that the product of a constant and a continuous function is continuous.

If the limit of the sum exists, then the limit of each component exists

$\lim_{n\rightarrow \infty} (a_n+b_n)=0$ $\lim_{n\rightarrow \infty} (b_n-c_n)=0$ imply $\lim_{n\rightarrow \infty} (a_n+c_n)=0$?

$\lim_{n\rightarrow \infty} (a_n+b_n)=0$ and $\lim_{n\rightarrow \infty} c_n=L$ imply $\lim_{n\rightarrow \infty} \exp(a_n)c_n-L\exp(-b_n)=0$

$\lim_{n\rightarrow \infty} (a_n-b_n)=0$ and $\lim_{n\rightarrow \infty} b_n=0$ imply $\lim_{n\rightarrow \infty}a_n=0$?

Compute $ \lim_{n\rightarrow \infty}\frac{\exp(x_j)}{n+\sum_{k=1}^n \exp(x_k)} $ with $x_k$ uniformly bounded

When to use L'Hospital's rule vs the limit shortcut

Finding integers and the limit of a sequence - from a 100 sequence and more (Russian book)

How is this proof for the scalar product rule of limits valid?

Calculating upper and lower limits for a linear function

Does $(1-e^{-y})^n $ converge as $n \to \infty$?

Prove that the following sequence converges

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