Question

What is $\lim_{n\to\infty}\frac{2^{\log(n^2)}}{\sqrt{n^3}}$?

score 98 · Answer 1 · 2018-10-30 11:25:08

98

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What is $\lim_{n\to\infty}\frac{2^{\log(n^2)}}{\sqrt{n^3}}$?

Published on 30 Oct 2018 - 11:25

score 45 · Answer 2 · 2018-10-30 11:58:42

45

Views

Is $\sqrt{(f(n)^2+g(n)^2)/{2}} = O(\max(f(n),g(n)))$

Published on 30 Oct 2018 - 11:58

score 90 · Answer 3 · 2018-10-30 12:54:22

90

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Master Theorem on $T_1(n) = 5 \cdot T_1 (\frac{n}{3}) + T_1(\frac{2n}{3}) + 3\cdot n$

Published on 30 Oct 2018 - 12:54

score 43 · Answer 4 · 2018-10-30 16:52:31

43

Views

From integral to $ \Theta\left(\sqrt{n}\left(\log{n} +1\right)\right)$

Published on 30 Oct 2018 - 16:52

score 2.6k · Answer 5 · 2018-10-30 19:15:12

2.6k

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Formal proof of $f(n) = \Theta(f(n/2))$

Published on 30 Oct 2018 - 19:15

score 40 · Answer 6 · 2018-10-31 00:36:59

40

Views

Showing $2^x$ is a lower bound

Published on 31 Oct 2018 - 0:36

score 87 · Answer 7 · 2026-03-25 11:04:43

87

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The asymptotic behavior of $\sum_{n=1}^x\sigma_a(n)\sigma_b(n)$

Published on 25 Mar 2026 - 11:04

score 54 · Answer 8 · 2018-10-31 17:18:35

54

Views

Asymptotic expression of $f(x) = \sum \dfrac{1}{n} \tanh(\frac{x}{n})$ as $x\to \infty$

Published on 31 Oct 2018 - 17:18

score 225 · Answer 9 · 2018-10-31 17:59:09

225

Views

Assuming $f(n)$ is non-decreasing and $f(n) = n^2$ where $n$ is odd, then $f(n) \in \Theta(n^2)$.

Published on 31 Oct 2018 - 17:59

score 43 · Answer 10 · 2018-10-31 18:34:47

43

Views

If $a(n) + b(n) \in \Omega(p(n))$, then $a(n) \in \Omega(p(n)) \vee b(n)\in \Omega(p(n))$.

Published on 31 Oct 2018 - 18:34

score 48 · Answer 11 · 2018-10-31 18:56:11

48

Views

If $a(n) + p(n) \in \Theta(b(n) + p(n))$, then $a(n) \in \Theta(b(n))$. True or False?

Published on 31 Oct 2018 - 18:56

score 392 · Answer 12 · 2026-03-25 06:10:45

392

Views

Picking the correct Ansatz for valid solutions in Asymptotic Methods

Published on 25 Mar 2026 - 6:10

score 173 · Answer 13 · 2018-11-01 01:00:27

173

Views

Asymptotic solution of Airy's equation using WKB

Published on 01 Nov 2018 - 1:00

score 1.3k · Answer 14 · 2018-11-01 06:59:58

1.3k

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Big-O notation: Prove that $3^x$ is $O(3^x - 2^x)$

Published on 01 Nov 2018 - 6:59

score 54 · Answer 15 · 2018-11-01 16:50:50

54

Views

Little-oh vs. $\ll$ notation

Published on 01 Nov 2018 - 16:50

List Question

What is $\lim_{n\to\infty}\frac{2^{\log(n^2)}}{\sqrt{n^3}}$?

Is $\sqrt{(f(n)^2+g(n)^2)/{2}} = O(\max(f(n),g(n)))$

Master Theorem on $T_1(n) = 5 \cdot T_1 (\frac{n}{3}) + T_1(\frac{2n}{3}) + 3\cdot n$

From integral to $ \Theta\left(\sqrt{n}\left(\log{n} +1\right)\right)$

Formal proof of $f(n) = \Theta(f(n/2))$

Showing $2^x$ is a lower bound

The asymptotic behavior of $\sum_{n=1}^x\sigma_a(n)\sigma_b(n)$

Asymptotic expression of $f(x) = \sum \dfrac{1}{n} \tanh(\frac{x}{n})$ as $x\to \infty$

Assuming $f(n)$ is non-decreasing and $f(n) = n^2$ where $n$ is odd, then $f(n) \in \Theta(n^2)$.

If $a(n) + b(n) \in \Omega(p(n))$, then $a(n) \in \Omega(p(n)) \vee b(n)\in \Omega(p(n))$.

If $a(n) + p(n) \in \Theta(b(n) + p(n))$, then $a(n) \in \Theta(b(n))$. True or False?

Picking the correct Ansatz for valid solutions in Asymptotic Methods

Asymptotic solution of Airy's equation using WKB

Big-O notation: Prove that $3^x$ is $O(3^x - 2^x)$

Little-oh vs. $\ll$ notation

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