Question

Find limit of $\sqrt{n^3 + 2n} - \sqrt{n^3 + 1}$ as $n$ goes to $+\infty$

score 100 · Answer 1 · 2018-10-08 17:29:26

100

Views

Find limit of $\sqrt{n^3 + 2n} - \sqrt{n^3 + 1}$ as $n$ goes to $+\infty$

Published on 08 Oct 2018 - 17:29

score 92 · Answer 2 · 2026-03-25 20:53:28

92

Views

Proof of inequality $|x \sin \alpha + y \cos \alpha| \leq \sqrt{x^2 + y^2}$

Published on 25 Mar 2026 - 20:53

score 475 · Answer 3 · 2026-03-25 06:02:02

475

Views

Coefficients of binomial continued fractions

Published on 25 Mar 2026 - 6:02

score 84 · Answer 4 · 2018-10-11 10:06:38

84

Views

Is the limit of $\cos \frac {1}{2(\sqrt{x +1} - \sqrt {x})} $as $x \rightarrow \infty$ is 0?

Published on 11 Oct 2018 - 10:06

score 33 · Answer 5 · 2018-10-11 14:18:30

33

Views

Proving that a limit equal 0 as $x \rightarrow \infty$ by epsilon delta definition.

Published on 11 Oct 2018 - 14:18

score 577 · Answer 6 · 2018-10-11 14:28:52

577

Views

How to calculate the limit $\lim_{n\rightarrow\infty}\left(\sqrt{4n+1}-\sqrt{n}-\sqrt{n+1}\right)$?

Published on 11 Oct 2018 - 14:28

score 79 · Answer 7 · 2018-10-12 16:22:30

79

Views

Not sure how to solve $\lim_\limits{x\to0}{{\sqrt{x^2+1}-1}\over\sqrt{x^2+16}-4}$

Published on 12 Oct 2018 - 16:22

score 279 · Answer 8 · 2026-03-25 07:48:48

279

Views

Definite integration of spherical Bessel function of radical argument

Published on 25 Mar 2026 - 7:48

score 84 · Answer 9 · 2018-10-14 02:28:58

84

Views

Show that $ Ax^2 + x + 1 = 0 $ has roots greater than $1$ given $-1<A<0$

Published on 14 Oct 2018 - 2:28

score 85 · Answer 10 · 2026-03-25 01:27:01

85

Views

What is the mathematical approach of inversing a function resulting in a piece-wise solution?

Published on 25 Mar 2026 - 1:27

score 405 · Answer 11 · 2026-03-25 18:47:16

405

Views

Maximize the value of $\sqrt{x-x^2}+\sqrt{cx-x^2}$ without using calculus

Published on 25 Mar 2026 - 18:47

score 153 · Answer 12 · 2018-10-14 16:14:16

153

Views

Inequality with choose function: $1\sqrt{\binom n1} + 2\sqrt{\binom n2}+3\sqrt{\binom n3}+\cdots+n\sqrt{\binom nn} < \sqrt{{2^{n-1}}{n^3}}$

Published on 14 Oct 2018 - 16:14

score 125 · Answer 13 · 2026-03-26 06:32:31

125

Views

Let $x$, $y$, $z$, $t$ are real numbers. $x+y+z+t=6$ and $\sqrt{1-x^2}+\sqrt{4-y^2}+\sqrt{9-z^2}+\sqrt{16-t^2}=8$ Find each value of them as a number.

Published on 26 Mar 2026 - 6:32

score 77 · Answer 14 · 2018-10-15 17:07:50

77

Views

Find count of this functions roots:$\sqrt{x+1}-x^2+1=0$

Published on 15 Oct 2018 - 17:07

score 75 · Answer 15 · 2026-03-25 06:19:49

75

Views

How to make squaring method of finding an inverse function to be invertible?

Published on 25 Mar 2026 - 6:19

List Question

Find limit of $\sqrt{n^3 + 2n} - \sqrt{n^3 + 1}$ as $n$ goes to $+\infty$

Proof of inequality $|x \sin \alpha + y \cos \alpha| \leq \sqrt{x^2 + y^2}$

Coefficients of binomial continued fractions

Is the limit of $\cos \frac {1}{2(\sqrt{x +1} - \sqrt {x})} $as $x \rightarrow \infty$ is 0?

Proving that a limit equal 0 as $x \rightarrow \infty$ by epsilon delta definition.

How to calculate the limit $\lim_{n\rightarrow\infty}\left(\sqrt{4n+1}-\sqrt{n}-\sqrt{n+1}\right)$?

Not sure how to solve $\lim_\limits{x\to0}{{\sqrt{x^2+1}-1}\over\sqrt{x^2+16}-4}$

Definite integration of spherical Bessel function of radical argument

Show that $ Ax^2 + x + 1 = 0 $ has roots greater than $1$ given $-1<A<0$

What is the mathematical approach of inversing a function resulting in a piece-wise solution?

Maximize the value of $\sqrt{x-x^2}+\sqrt{cx-x^2}$ without using calculus

Inequality with choose function: $1\sqrt{\binom n1} + 2\sqrt{\binom n2}+3\sqrt{\binom n3}+\cdots+n\sqrt{\binom nn} < \sqrt{{2^{n-1}}{n^3}}$

Let $x$, $y$, $z$, $t$ are real numbers. $x+y+z+t=6$ and $\sqrt{1-x^2}+\sqrt{4-y^2}+\sqrt{9-z^2}+\sqrt{16-t^2}=8$ Find each value of them as a number.

Find count of this functions roots:$\sqrt{x+1}-x^2+1=0$

How to make squaring method of finding an inverse function to be invertible?

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