Sunday, 8 March 2015

limits - How to evaluate limxto0fracsin2left(fracx2right)fracx24ex2+ex22?

lim



After evaluating the limit as x \to 0, I noticed that the problem comes up to be in an indeterminate form of 0/0. I immediately utilized the L'Hospital Rule by differentiating both the numerator and denominator.



However, after using L'Hospital rule for 5-6 times, I noticed that the question will go through a loop of 0/0 indeterminants.



In my second attempt,
I have tried multiplying \exp(x^2) in both the numerator and denominator with hopes to balance out the \exp(x^{-2}). However, an indeterminant is 0/0 still resulting.




Any help would be appreciated, thank you all!

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