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November 7th, 2017, 02:10 AM   #1
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How to calculate this limit?

Hi! I know that the value of this limit is 1, but I do not know how to calculate it:
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February 21st, 2018, 12:10 AM   #2
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Sorry about delay
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February 27th, 2018, 02:45 PM   #3
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Hi,

First, as n approaches infinity, the term (y/n)^2 approaches 1; hence, the term (1+(y/n)^2) approaches 1. Even though n/2 will approach infinity, 1 to any power equals 1.

Hope that helps!
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February 27th, 2018, 04:21 PM   #4
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I would say that the limit is $e^y$.
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February 27th, 2018, 06:08 PM   #5
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The limit is 1, but matheagl365's argument is flawed.

Consider the natural logarithm of the expression. It's easy to show that its limit is zero.
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February 27th, 2018, 10:36 PM   #6
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Quote:
Originally Posted by v8archie View Post
I would say that the limit is $e^y$.
wait, you're right! but how??
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February 27th, 2018, 11:25 PM   #7
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skipjack has the correct answer. You can get the expression by taking the natural log of both sides of L = lim(...).

-Dan
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February 27th, 2018, 11:33 PM   #8
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let's be careful here

$\lim \limits_{n\to \infty}~\left(1+\left(\frac y n\right)^2\right)^{\frac n 2} = 1$

$\lim \limits_{n\to \infty}~\left(\left(1+\frac y n\right)^2\right)^{\frac n 2} = e^y$
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March 1st, 2018, 03:10 PM   #9
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oh, thanks for pointing that out.
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