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August 28th, 2017, 10:45 AM   #1
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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.
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August 28th, 2017, 11:38 AM   #2
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MacLaurin series.
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August 28th, 2017, 11:40 AM   #3
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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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