Question

Solving this limit $\lim_{x\to 3}\frac{x^2-9-3+\sqrt{x+6}}{x^2-9}$.

score 458 · Answer 1 · 2016-01-17 12:22:18

458

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Solving this limit $\lim_{x\to 3}\frac{x^2-9-3+\sqrt{x+6}}{x^2-9}$.

Published on 17 Jan 2016 - 12:22

score 197 · Answer 2 · 2026-03-31 11:58:07

197

Views

Prove that $ \sum\limits_{cyc} \sqrt{\cot{A}+\cot{B}} \ge 2\sqrt2$

Published on 31 Mar 2026 - 11:58

score 173 · Answer 3 · 2026-03-31 09:39:20

173

Views

Prove that $\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+d}+\frac{d}{d+a}\geq1+4\sqrt{\frac{abcd}{(a+b)(b+c)(c+d)(d+a)}}$

Published on 31 Mar 2026 - 9:39

score 908 · Answer 4 · 2016-01-19 16:01:41

908

Views

How to show $\frac{1}{2\sqrt{2} + \sqrt{3}} = \frac{2\sqrt{2} - \sqrt{3}}{5}$?

Published on 19 Jan 2016 - 16:01

score 8.3k · Answer 5 · 2016-01-19 21:58:10

8.3k

Views

Why do I get one extra wrong solution when solving $2-x=-\sqrt{x}$?

Published on 19 Jan 2016 - 21:58

score 368 · Answer 6 · 2016-01-22 11:29:16

368

Views

Calculating $\lim_{n\to\infty}\sqrt[n]{ \sqrt[n]{n} - 1 }$

Published on 22 Jan 2016 - 11:29

score 146 · Answer 7 · 2016-01-23 08:08:07

146

Views

Integral with simple fractions: $\int_\ \frac{\cos x }{\sin x \sqrt{1+\cos^2x}} \, dx$

Published on 23 Jan 2016 - 8:08

score 110 · Answer 8 · 2026-04-04 04:55:45

110

Views

Roots of $x^3-x+1$

Published on 04 Apr 2026 - 4:55

score 69 · Answer 9 · 2016-01-24 05:41:55

69

Views

Evaluate the limit of function $\lim_{x\to\infty}\frac{(9x^2+1)^{1/2}}{x+2}.$

Published on 24 Jan 2016 - 5:41

score 10k · Answer 10 · 2016-01-24 11:03:41

10k

Views

How do I simplify and evaluate the limit of $(\sqrt x - 1)/(\sqrt[3] x - 1)$ as $x\to 1$?

Published on 24 Jan 2016 - 11:03

score 119 · Answer 11 · 2016-01-25 19:08:36

119

Views

Solving a radical equation with trinomials on both sides

Published on 25 Jan 2016 - 19:08

score 101 · Answer 12 · 2016-01-25 23:25:57

101

Views

$x\in\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$, s.t. $x^2=p+q\sqrt{30}$

Published on 25 Jan 2016 - 23:25

score 221 · Answer 13 · 2026-04-04 12:00:48

221

Views

Prove $\frac{1\cdot 3\cdots(2n-1)}{2\cdot 4 \cdots(2n)}<\frac{1}{\sqrt{2n+1}}$, $n\ge 1$

Published on 04 Apr 2026 - 12:00

score 77 · Answer 14 · 2026-04-05 22:37:26

77

Views

Squaring a binominal

Published on 05 Apr 2026 - 22:37

score 614 · Answer 15 · 2026-03-29 18:15:20

614

Views

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

Published on 29 Mar 2026 - 18:15

List Question

Solving this limit $\lim_{x\to 3}\frac{x^2-9-3+\sqrt{x+6}}{x^2-9}$.

Prove that $ \sum\limits_{cyc} \sqrt{\cot{A}+\cot{B}} \ge 2\sqrt2$

Prove that $\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+d}+\frac{d}{d+a}\geq1+4\sqrt{\frac{abcd}{(a+b)(b+c)(c+d)(d+a)}}$

How to show $\frac{1}{2\sqrt{2} + \sqrt{3}} = \frac{2\sqrt{2} - \sqrt{3}}{5}$?

Why do I get one extra wrong solution when solving $2-x=-\sqrt{x}$?

Calculating $\lim_{n\to\infty}\sqrt[n]{ \sqrt[n]{n} - 1 }$

Integral with simple fractions: $\int_\ \frac{\cos x }{\sin x \sqrt{1+\cos^2x}} \, dx$

Roots of $x^3-x+1$

Evaluate the limit of function $\lim_{x\to\infty}\frac{(9x^2+1)^{1/2}}{x+2}.$

How do I simplify and evaluate the limit of $(\sqrt x - 1)/(\sqrt[3] x - 1)$ as $x\to 1$?

Solving a radical equation with trinomials on both sides

$x\in\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$, s.t. $x^2=p+q\sqrt{30}$

Prove $\frac{1\cdot 3\cdots(2n-1)}{2\cdot 4 \cdots(2n)}<\frac{1}{\sqrt{2n+1}}$, $n\ge 1$

Squaring a binominal

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

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