Question

Prove or disprove : $\sqrt{1 + \sqrt{4+\sqrt{16+\sqrt{256...}}}} = \sqrt{2+\sqrt{5}}$

score 732 · Answer 1 · 2026-03-30 13:39:13

732

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Prove or disprove : $\sqrt{1 + \sqrt{4+\sqrt{16+\sqrt{256...}}}} = \sqrt{2+\sqrt{5}}$

Published on 30 Mar 2026 - 13:39

score 202 · Answer 2 · 2017-10-28 07:30:16

202

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Evaluate $\lim_{n\rightarrow \infty}4\sqrt{n}\sin (\pi\sqrt{4n^2+\sqrt{n}})$

Published on 28 Oct 2017 - 7:30

score 110 · Answer 3 · 2017-10-29 10:42:57

110

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Solving $\lim_{x\rightarrow 0} \frac{\frac{1}{1+x}- \cos x}{x}$ without L'Hôpital

Published on 29 Oct 2017 - 10:42

score 210 · Answer 4 · 2017-10-29 15:30:03

210

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$\lim_{ x \to\frac\pi4 } \frac{1-\tan(x)}{\sin(x)-\cos(x)}$ without L'Hospital rule

Published on 29 Oct 2017 - 15:30

score 118 · Answer 5 · 2017-10-29 16:43:32

118

Views

Using manual approximations in limits?

Published on 29 Oct 2017 - 16:43

score 34 · Answer 6 · 2017-10-29 23:38:37

34

Views

Does the limit change under some disturbance.

Published on 29 Oct 2017 - 23:38

score 916 · Answer 7 · 2017-10-30 15:07:29

916

Views

Find the limit of the complex function.

Published on 30 Oct 2017 - 15:07

score 217 · Answer 8 · 2017-11-01 12:54:44

217

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without L'Hospital: $\lim _{x\to 0}\frac{\sqrt[5]{1+3x^4}-\sqrt{1-2x}}{\sqrt[3]{1+x}-\sqrt{1+x}}$

Published on 01 Nov 2017 - 12:54

score 139 · Answer 9 · 2017-11-01 18:17:07

139

Views

How to compute $\lim_{x\to\infty} \frac{2^x}{x^{200}}$?

Published on 01 Nov 2017 - 18:17

score 270 · Answer 10 · 2017-11-02 14:39:06

270

Views

Proving $\lim_{x \to \infty}\frac{\ln x}{x^r}=0$ and $\lim_{x \to 0^+}x^r\ln x=0$ for $r>0$

Published on 02 Nov 2017 - 14:39

score 68 · Answer 11 · 2017-11-02 14:51:36

68

Views

Prove non-existence of $\lim_{n\to\infty}(-1)^n\frac{2^n+4n+6}{2^n(\sqrt[n]{5}-1)}$

Published on 02 Nov 2017 - 14:51

score 445 · Answer 12 · 2017-11-02 17:00:52

445

Views

How does one go about $\lim_{y\to x} \frac{x^n-y^n}{x-y}$?

Published on 02 Nov 2017 - 17:00

score 67 · Answer 13 · 2017-11-03 09:57:24

67

Views

Determining the limit of a function containing $(x-1)^5$ without l'hopital`s rule.

Published on 03 Nov 2017 - 9:57

score 136 · Answer 14 · 2017-11-03 10:22:42

136

Views

How do I solve $ \lim\limits_{n \to \infty}2\left(1-\frac {1}{n+1}\right)^n$?

Published on 03 Nov 2017 - 10:22

score 44 · Answer 15 · 2017-11-04 17:43:32

44

Views

limit of a function as $x$ goes to $0$

Published on 04 Nov 2017 - 17:43

List Question

Prove or disprove : $\sqrt{1 + \sqrt{4+\sqrt{16+\sqrt{256...}}}} = \sqrt{2+\sqrt{5}}$

Evaluate $\lim_{n\rightarrow \infty}4\sqrt{n}\sin (\pi\sqrt{4n^2+\sqrt{n}})$

Solving $\lim_{x\rightarrow 0} \frac{\frac{1}{1+x}- \cos x}{x}$ without L'Hôpital

$\lim_{ x \to\frac\pi4 } \frac{1-\tan(x)}{\sin(x)-\cos(x)}$ without L'Hospital rule

Using manual approximations in limits?

Does the limit change under some disturbance.

Find the limit of the complex function.

without L'Hospital: $\lim _{x\to 0}\frac{\sqrt[5]{1+3x^4}-\sqrt{1-2x}}{\sqrt[3]{1+x}-\sqrt{1+x}}$

How to compute $\lim_{x\to\infty} \frac{2^x}{x^{200}}$?

Proving $\lim_{x \to \infty}\frac{\ln x}{x^r}=0$ and $\lim_{x \to 0^+}x^r\ln x=0$ for $r>0$

Prove non-existence of $\lim_{n\to\infty}(-1)^n\frac{2^n+4n+6}{2^n(\sqrt[n]{5}-1)}$

How does one go about $\lim_{y\to x} \frac{x^n-y^n}{x-y}$?

Determining the limit of a function containing $(x-1)^5$ without l'hopital`s rule.

How do I solve $ \lim\limits_{n \to \infty}2\left(1-\frac {1}{n+1}\right)^n$?

limit of a function as $x$ goes to $0$

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