February 23rd, 2019, 07:55 AM  #1 
Newbie Joined: Jan 2019 From: Athens Posts: 5 Thanks: 0  Limit Calculation
Hi, I am trying to solve the following limit $\displaystyle \lim_{x\to\infty}\cos\left(\!\frac{\pi\sqrt{x^4 + 7}}{6x^2 + 5}\right)$ https://drive.google.com/open?id=1ll...XvBmLta1ozBcCW Any help is welcome!! Last edited by skipjack; March 26th, 2019 at 12:49 AM. 
February 23rd, 2019, 08:35 AM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 647 Thanks: 94 
You can set the limit inside the $\displaystyle \cos$function .

February 23rd, 2019, 05:56 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,554 Thanks: 1403 
$\lim \limits_{x\to \infty} \cos\left(\dfrac{\pi \sqrt{x^4+7}}{6x^2+5}\right) = $ $\lim \limits_{x\to \infty} \cos\left(\dfrac{\pi \sqrt{1+7x^{4}}}{6+5x^{2}}\right) =$ $\cos\left(\dfrac{\pi}{6}\right) = \dfrac{\sqrt{3}}{2}$ 

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