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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? $\displaystyle \lim_{x\to 0} (\cos x+(x^2-1)^{1/3})/(x\sin(x^2)-x(e^x-1))$ 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: 6,973 Thanks: 2296 Math Focus: Mainly analysis and algebra MacLaurin series.
 August 28th, 2017, 11:40 AM #3 Global Moderator   Joined: Dec 2006 Posts: 18,061 Thanks: 1396 The limit is 1/6, which is what W|A gives if you click to tell it to use the real-valued cube root. Are you allowed to use de l'Hôpital's rule to obtain the limit? If not, find the Maclaurin series for the numerator and the denominator.

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