Question

The limit as $x \to \infty$ of $ \frac {\sqrt{x+ \sqrt{ x+\sqrt x}} }{\sqrt{x+1}}$

score 6.4k · Answer 1 · 2026-03-30 04:41:55

6.4k

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The limit as $x \to \infty$ of $ \frac {\sqrt{x+ \sqrt{ x+\sqrt x}} }{\sqrt{x+1}}$

Published on 30 Mar 2026 - 4:41

score 5.9k · Answer 2 · 2026-03-30 04:41:30

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Find the value of : $\lim_{x\to\infty} \sqrt{x+\sqrt{x}}-\sqrt{x}$

Published on 30 Mar 2026 - 4:41

score 171 · Answer 3 · 2013-10-13 14:41:54

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How would I evaluate this limit? $\lim_{x\to 3+} \frac{x-3}{\sqrt{x^2-9}}$

Published on 13 Oct 2013 - 14:41

score 264 · Answer 4 · 2013-10-13 20:19:51

264

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Can't solve following limit: $\lim_{x \to \infty}x \left( \sqrt[3]{5+8x^3} - 2x\right)$

Published on 13 Oct 2013 - 20:19

score 1.5k · Answer 5 · 2026-03-27 00:02:05

1.5k

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Algebraic numbers that cannot be expressed using integers and elementary functions

Published on 27 Mar 2026 - 0:02

score 109 · Answer 6 · 2013-10-15 04:26:06

109

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How to solve $ 2x-3-2x^{ -1/2 }= 0 $ for $x$?

Published on 15 Oct 2013 - 4:26

score 79 · Answer 7 · 2013-10-18 08:25:28

79

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determine the radical $\sqrt{m\mathbb{Z}}$

Published on 18 Oct 2013 - 8:25

score 2.2k · Answer 8 · 2013-10-18 19:03:01

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system of equations $\sqrt{x}+y = 11$ and $x+\sqrt{y} = 7$.

Published on 18 Oct 2013 - 19:03

score 81 · Answer 9 · 2013-10-19 15:03:06

81

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The limit of the ratio of ${(n+1)^{\frac 12}-(n^3+1)^{\frac 13}}$ and ${(n+1)^{\frac 14}-(n^5+1)^{\frac 15}}$

Published on 19 Oct 2013 - 15:03

score 782 · Answer 10 · 2026-03-30 03:39:16

782

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Prove $_4F_3(1/8,3/8,5/8,7/8;1/4,1/2,3/4;1/2)=\frac{\sqrt{2-\sqrt2+\sqrt{2-\sqrt2}}+\sqrt{2+\sqrt2+\sqrt{2+\sqrt2}}}{2\,\sqrt2}$

Published on 30 Mar 2026 - 3:39

score 98 · Answer 11 · 2013-10-19 17:05:34

98

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Evaluation of $\lim_{x\to -2} \frac{\sqrt[3]{x - 6} + 2}{x+2}$

Published on 19 Oct 2013 - 17:05

score 1k · Answer 12 · 2013-10-19 18:42:18

1k

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Find the limit of $\sum\limits_{k=1}^n\left(\sqrt{1+\frac{k}{n^2}}-1\right)$

Published on 19 Oct 2013 - 18:42

score 525 · Answer 13 · 2013-10-20 12:17:15

525

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How prove this $x+y=0$ if $\left(\sqrt{y^2-x^3}-x\right)\left(\sqrt{x^2+y^3}-y\right)=y^3$

Published on 20 Oct 2013 - 12:17

score 5.2k · Answer 14 · 2013-10-24 10:36:16

5.2k

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Is there any simple method to calculate $\sqrt x$ without using logarithm

Published on 24 Oct 2013 - 10:36

score 771 · Answer 15 · 2013-10-24 15:05:35

771

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Evaluating a limit for a odd rooted radical

Published on 24 Oct 2013 - 15:05

List Question

The limit as $x \to \infty$ of $ \frac {\sqrt{x+ \sqrt{ x+\sqrt x}} }{\sqrt{x+1}}$

Find the value of : $\lim_{x\to\infty} \sqrt{x+\sqrt{x}}-\sqrt{x}$

How would I evaluate this limit? $\lim_{x\to 3+} \frac{x-3}{\sqrt{x^2-9}}$

Can't solve following limit: $\lim_{x \to \infty}x \left( \sqrt[3]{5+8x^3} - 2x\right)$

Algebraic numbers that cannot be expressed using integers and elementary functions

How to solve $ 2x-3-2x^{ -1/2 }= 0 $ for $x$?

determine the radical $\sqrt{m\mathbb{Z}}$

system of equations $\sqrt{x}+y = 11$ and $x+\sqrt{y} = 7$.

The limit of the ratio of ${(n+1)^{\frac 12}-(n^3+1)^{\frac 13}}$ and ${(n+1)^{\frac 14}-(n^5+1)^{\frac 15}}$

Prove $_4F_3(1/8,3/8,5/8,7/8;1/4,1/2,3/4;1/2)=\frac{\sqrt{2-\sqrt2+\sqrt{2-\sqrt2}}+\sqrt{2+\sqrt2+\sqrt{2+\sqrt2}}}{2\,\sqrt2}$

Evaluation of $\lim_{x\to -2} \frac{\sqrt[3]{x - 6} + 2}{x+2}$

Find the limit of $\sum\limits_{k=1}^n\left(\sqrt{1+\frac{k}{n^2}}-1\right)$

How prove this $x+y=0$ if $\left(\sqrt{y^2-x^3}-x\right)\left(\sqrt{x^2+y^3}-y\right)=y^3$

Is there any simple method to calculate $\sqrt x$ without using logarithm

Evaluating a limit for a odd rooted radical

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