Question

Is a two-part function differentiable if the limit of one part equals the value at the other part?

score 22 · Answer 1 · 2026-04-13 17:27:29

22

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Is a two-part function differentiable if the limit of one part equals the value at the other part?

Published on 13 Apr 2026 - 17:27

score 184 · Answer 2 · 2026-04-16 19:10:50

184

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Find the general term of the sequence $a_n = (0, 3, 1/2 , 5/3 , 2/3 , 7/5 , 3/4 , ...)$. Then find the limit of this sequence.

Published on 16 Apr 2026 - 19:10

score 84 · Answer 3 · 2026-04-16 12:06:32

84

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If $u_n = (1+\frac{1}{n^2})\ldots(1+\frac{n}{n^2})$ then $\lim u_n=\sqrt{e}$?

Published on 16 Apr 2026 - 12:06

score 4.4k · Answer 4 · 2026-04-15 07:39:59

4.4k

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Proof that $\lim_{x\to \infty} (1+(x/n))^n = e^x$ Using Monotone Convergence Theorem

Published on 15 Apr 2026 - 7:39

score 114 · Answer 5 · 2026-04-15 21:30:30

114

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Limit of $S_n = \sum_{i = 1}^n \frac{i^k}{n^{k+1}} $

Published on 15 Apr 2026 - 21:30

score 26 · Answer 6 · 2026-04-14 04:03:18

26

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Is this method for evaluating this complex limit correct?

Published on 14 Apr 2026 - 4:03

score 60 · Answer 7 · 2026-04-16 04:00:55

Determination of limit of a nonconstant function $f: \mathbb{R} \to \mathbb{R}$ satisfying $f(x) = f(x + 2)$ for every real number $x$

score 45 · Answer 8 · 2026-04-14 11:42:09

45

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How to show that this specific limit exists in this proof?

Published on 14 Apr 2026 - 11:42

score 103 · Answer 9 · 2026-04-12 09:31:06

103

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How can I solve this limit?(From AMM)

Published on 12 Apr 2026 - 9:31

score 41 · Answer 10 · 2026-04-17 11:42:22

41

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$\lim_{N\to\infty}\sum_{i=1}^N \frac{\log_e^i}{i} /(\log_e^N)^2 $ =

Published on 17 Apr 2026 - 11:42

score 141 · Answer 11 · 2026-04-13 21:09:44

141

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How to prove this specific function has limit either $\infty$ or 0?

Published on 13 Apr 2026 - 21:09

score 49 · Answer 12 · 2026-04-11 14:50:32

49

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Is this a proof rigorous enough? (Definition of the limit)

Published on 11 Apr 2026 - 14:50

score 34 · Answer 13 · 2026-04-15 22:48:02

34

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Confirmation of Proof: $\forall a,b \in\mathbb{R}, \ \sum_{n=0}^\infty \frac{a}{b^n} = \frac{ab}{b-1}\Leftrightarrow \frac b2\in(1, a].$

Published on 15 Apr 2026 - 22:48

score 141 · Answer 14 · 2026-04-14 17:07:49

141

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calculate the limit $\lim_{n \to \infty} n!^{\frac1n}$

Published on 14 Apr 2026 - 17:07

score 68 · Answer 15 · 2026-04-12 15:40:36

68

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The mathematical approach to the infinity in calculus

Published on 12 Apr 2026 - 15:40

List Question

Is a two-part function differentiable if the limit of one part equals the value at the other part?

Find the general term of the sequence $a_n = (0, 3, 1/2 , 5/3 , 2/3 , 7/5 , 3/4 , ...)$. Then find the limit of this sequence.

If $u_n = (1+\frac{1}{n^2})\ldots(1+\frac{n}{n^2})$ then $\lim u_n=\sqrt{e}$?

Proof that $\lim_{x\to \infty} (1+(x/n))^n = e^x$ Using Monotone Convergence Theorem

Limit of $S_n = \sum_{i = 1}^n \frac{i^k}{n^{k+1}} $

Is this method for evaluating this complex limit correct?

Determination of limit of a nonconstant function $f: \mathbb{R} \to \mathbb{R}$ satisfying $f(x) = f(x + 2)$ for every real number $x$

How to show that this specific limit exists in this proof?

How can I solve this limit?(From AMM)

$\lim_{N\to\infty}\sum_{i=1}^N \frac{\log_e^i}{i} /(\log_e^N)^2 $ =

How to prove this specific function has limit either $\infty$ or 0?

Is this a proof rigorous enough? (Definition of the limit)

Confirmation of Proof: $\forall a,b \in\mathbb{R}, \ \sum_{n=0}^\infty \frac{a}{b^n} = \frac{ab}{b-1}\Leftrightarrow \frac b2\in(1, a].$

calculate the limit $\lim_{n \to \infty} n!^{\frac1n}$

The mathematical approach to the infinity in calculus

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