My Math Forum How could I solve this limit?

 Real Analysis Real Analysis Math Forum

 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: 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 W|A gives if you click to tell it to use the real-valued 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.

 Tags limit, solve

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post valonidv7 Calculus 6 May 29th, 2016 10:37 AM complicatemodulus Calculus 15 September 3rd, 2015 07:49 AM Bhushan Calculus 7 May 13th, 2013 07:40 PM chocolatesheep Calculus 4 December 3rd, 2012 09:58 AM kevpb Calculus 1 January 20th, 2012 01:27 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top