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August 28th, 2017, 10:45 AM  #1 
Newbie Joined: Aug 2017 From: Milan Posts: 3 Thanks: 0  How could I solve this limit?
$\displaystyle \lim_{x\to 0} (\cos x+(x^21)^{1/3})/(x\sin(x^2)x(e^x1))$ I used asymptotic analysis and the limit converges to 1/2, but wolframalpha gives complex solution. Thank you. Last edited by skipjack; August 28th, 2017 at 11:42 AM. 
August 28th, 2017, 11:38 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,344 Thanks: 2466 Math Focus: Mainly analysis and algebra 
MacLaurin series.

August 28th, 2017, 11:40 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,299 Thanks: 1688 
The limit is 1/6, which is what WA gives if you click to tell it to use the realvalued cube root. Are you allowed to use de l'HÃ´pital's rule to obtain the limit? If not, find the Maclaurin series for the numerator and the denominator. 

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