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For what real values of $p$ does $lim_{xrightarrowinfty}frac{1}{x^p+x^{-p}}$ exist and is finite?

Is $lim_{n rightarrow infty} sum_{k = 1}^infty frac{(1-epsilon(n))^k}{k}$ Finite When $epsilon(n) rightarrow 0$?Calculate $lim_{nrightarrow infty}frac{log{binom{n}{n_1}}}{n}$Show that $ lim_{n rightarrow infty} frac{n!}{2^{n}} = infty $For what $k$ does $lim_{x to-infty} frac{5^{kx}-1}{5^{-2x} + 1}$ exist?For what $ain mathbb{R}$ does this limit exist?Finding the limit of $lim_{nrightarrowinfty}(frac{1}{6}+frac{1}{24}+frac{1}{60}+frac{1}{120}+…[text{upto n times}])$When does equality for $x_n < y_n Rightarrow lim_{n rightarrow infty} x_n leq lim_{n rightarrow infty} y_n$ hold?For what values of $a$ and $b$ does $lim_{xrightarrow infty}(sqrt{x^2+x+1}-ax-b)=1$?Why does $lim_{nrightarrow infty }left(1+frac{cos(npi )}{n}right)^{n}$ NOT exist?What real $p$ makes this limit exists and be finite?

0

$begingroup$

For what real values of $p$ does exist and is finite the limit $lim_{xrightarrowinfty}frac{1}{x^p+x^{-p}}$?

I know that $frac{1}{x^p+x^{-p}}leqfrac{1}{2}$. I think that this happens only for $p=0$ and I have a feeling this is the only value, but I am unsure on how to develop my response solely from this information. Any help?

calculus limits limits-without-lhopital

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edited Mar 15 at 10:25

StubbornAtom

6,30831440

asked Mar 15 at 7:58

user651692

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add a comment | 

0

$begingroup$

For what real values of $p$ does exist and is finite the limit $lim_{xrightarrowinfty}frac{1}{x^p+x^{-p}}$?

I know that $frac{1}{x^p+x^{-p}}leqfrac{1}{2}$. I think that this happens only for $p=0$ and I have a feeling this is the only value, but I am unsure on how to develop my response solely from this information. Any help?

calculus limits limits-without-lhopital

share|cite|improve this question

edited Mar 15 at 10:25

StubbornAtom

6,30831440

asked Mar 15 at 7:58

user651692

$endgroup$

add a comment | 

$begingroup$

For what real values of $p$ does exist and is finite the limit $lim_{xrightarrowinfty}frac{1}{x^p+x^{-p}}$?

I know that $frac{1}{x^p+x^{-p}}leqfrac{1}{2}$. I think that this happens only for $p=0$ and I have a feeling this is the only value, but I am unsure on how to develop my response solely from this information. Any help?

calculus limits limits-without-lhopital

share|cite|improve this question

edited Mar 15 at 10:25

StubbornAtom

6,30831440

asked Mar 15 at 7:58

user651692

$endgroup$

share|cite|improve this question

edited Mar 15 at 10:25

StubbornAtom

6,30831440

asked Mar 15 at 7:58

user651692

share|cite|improve this question

edited Mar 15 at 10:25

StubbornAtom

6,30831440

asked Mar 15 at 7:58

user651692

edited Mar 15 at 10:25

StubbornAtom

6,30831440

edited Mar 15 at 10:25

StubbornAtom

6,30831440

1 Answer
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$begingroup$

The limit is $0$ for $p neq 0$ and $frac 1 2$ for $p=0$. [For example, if $p>0$ then $x^{p} to infty$ and $x^{-p} to 0$ so $x^{p}+x^{-p} to infty$, etc].

share|cite|improve this answer

answered Mar 15 at 8:00

Kavi Rama MurthyKavi Rama Murthy

70.1k53170

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1

$begingroup$

The limit is $0$ for $p neq 0$ and $frac 1 2$ for $p=0$. [For example, if $p>0$ then $x^{p} to infty$ and $x^{-p} to 0$ so $x^{p}+x^{-p} to infty$, etc].

share|cite|improve this answer

answered Mar 15 at 8:00

Kavi Rama MurthyKavi Rama Murthy

70.1k53170

$endgroup$

add a comment | 

1

$begingroup$

The limit is $0$ for $p neq 0$ and $frac 1 2$ for $p=0$. [For example, if $p>0$ then $x^{p} to infty$ and $x^{-p} to 0$ so $x^{p}+x^{-p} to infty$, etc].

share|cite|improve this answer

answered Mar 15 at 8:00

Kavi Rama MurthyKavi Rama Murthy

70.1k53170

$endgroup$

add a comment | 

$begingroup$

The limit is $0$ for $p neq 0$ and $frac 1 2$ for $p=0$. [For example, if $p>0$ then $x^{p} to infty$ and $x^{-p} to 0$ so $x^{p}+x^{-p} to infty$, etc].

share|cite|improve this answer

answered Mar 15 at 8:00

Kavi Rama MurthyKavi Rama Murthy

70.1k53170

$endgroup$

share|cite|improve this answer

answered Mar 15 at 8:00

Kavi Rama MurthyKavi Rama Murthy

70.1k53170

answered Mar 15 at 8:00

Kavi Rama MurthyKavi Rama Murthy

70.1k53170

answered Mar 15 at 8:00

Kavi Rama MurthyKavi Rama Murthy

70.1k53170