Friday, March 1, 2019

calculus - find limxto1fraclnxx+1epi(x1)+sin(pix)1

The answer choices available are:


(a) 1π -------- (b)1π1


(c) 1π2 -------- (d) undefined



You obviously can't solve the limit straightforwardly, because it gives you an indeterminate form (0/0), right? So I used L'Hôpital's rule, taking the derivative of the numerator and the denominator before plugging in x=1.


Derivative of the numerator: 1x1


Derivative of the denominator: π(eπ(x1)+cos(πx))


However, the numerator remains unavoidably equal to zero. Am I doing something wrong, glancing over something really obvious, or are the answer choices wrong? Any help would be greatly appreciated.

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