Question

Find derivative of $f(x)=\frac{1}{\sqrt{x+2}}$ by definition

score 261 · Answer 1 · 2014-10-22 21:35:53

261

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Find derivative of $f(x)=\frac{1}{\sqrt{x+2}}$ by definition

Published on 22 Oct 2014 - 21:35

score 5.9k · Answer 2 · 2026-03-25 11:06:40

5.9k

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If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?

Published on 25 Mar 2026 - 11:06

score 213 · Answer 3 · 2026-03-25 11:16:52

213

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Prove that $(\sqrt3+2)^m$ is not a natural number for all natural numbers $m≥1$

Published on 25 Mar 2026 - 11:16

score 590 · Answer 4 · 2026-03-25 11:11:45

590

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Show that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational

Published on 25 Mar 2026 - 11:11

score 181 · Answer 5 · 2014-10-28 12:35:26

181

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What does 8 root 2.5 ($\sqrt[8]{2.5}$) mean?

Published on 28 Oct 2014 - 12:35

score 2.7k · Answer 6 · 2026-03-26 19:20:00

2.7k

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How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$?

Published on 26 Mar 2026 - 19:20

score 1.1k · Answer 7 · 2026-03-28 16:56:52

1.1k

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Using the squeeze theorem to determine a limit $\lim_{n\to\infty} (n!)^{\frac{1}{n^2}}$

Published on 28 Mar 2026 - 16:56

score 188 · Answer 8 · 2014-10-29 17:03:28

188

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Limit $\lim_{n \rightarrow \infty} (A_1^n + ... A_k^n)^{1/n}= \max\{ A_1, ..., A_k\}$

Published on 29 Oct 2014 - 17:03

score 122 · Answer 9 · 2026-03-25 11:16:32

122

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Find the values of $k$ for which $\sqrt{1+\frac{k}{n}}$ is irrational for all $n\in\mathbb N$

Published on 25 Mar 2026 - 11:16

score 12.7k · Answer 10 · 2026-03-22 18:30:41

12.7k

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Difficult denomiator rationalization questions

Published on 22 Mar 2026 - 18:30

score 129 · Answer 11 · 2026-03-25 11:16:35

129

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Is $\sqrt{m}$ irrational iff at least one prime occurs with an odd exponent in the factorisation of $m$?

Published on 25 Mar 2026 - 11:16

score 89 · Answer 12 · 2014-11-01 20:16:31

89

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Prove that $\sqrt[n]n>\sqrt[n+1]{n+1}$ for all $n \geq 3$

Published on 01 Nov 2014 - 20:16

score 415 · Answer 13 · 2014-11-02 20:44:27

415

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Proving $\sum^{n}_{k=1} \frac{1}{\sqrt{k}}>\sqrt{n}$ by induction

Published on 02 Nov 2014 - 20:44

score 147 · Answer 14 · 2026-03-28 11:52:10

147

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$\sqrt{1\pm10\varepsilon+\varepsilon^2}=1\pm P(\varepsilon)$. Is there a better way than mine to find $P(\varepsilon)$?

Published on 28 Mar 2026 - 11:52

score 152 · Answer 15 · 2014-11-03 04:28:37

152

Views

How can I show if this series diverges or converges: $\sum_{n=1}^\infty \frac{1}{\sqrt{n+2}+\sqrt{n}}$?

Published on 03 Nov 2014 - 4:28

List Question

Find derivative of $f(x)=\frac{1}{\sqrt{x+2}}$ by definition

If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?

Prove that $(\sqrt3+2)^m$ is not a natural number for all natural numbers $m≥1$

Show that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational

What does 8 root 2.5 ($\sqrt[8]{2.5}$) mean?

How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$?

Using the squeeze theorem to determine a limit $\lim_{n\to\infty} (n!)^{\frac{1}{n^2}}$

Limit $\lim_{n \rightarrow \infty} (A_1^n + ... A_k^n)^{1/n}= \max\{ A_1, ..., A_k\}$

Find the values of $k$ for which $\sqrt{1+\frac{k}{n}}$ is irrational for all $n\in\mathbb N$

Difficult denomiator rationalization questions

Is $\sqrt{m}$ irrational iff at least one prime occurs with an odd exponent in the factorisation of $m$?

Prove that $\sqrt[n]n>\sqrt[n+1]{n+1}$ for all $n \geq 3$

Proving $\sum^{n}_{k=1} \frac{1}{\sqrt{k}}>\sqrt{n}$ by induction

$\sqrt{1\pm10\varepsilon+\varepsilon^2}=1\pm P(\varepsilon)$. Is there a better way than mine to find $P(\varepsilon)$?

How can I show if this series diverges or converges: $\sum_{n=1}^\infty \frac{1}{\sqrt{n+2}+\sqrt{n}}$?

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