Question

This involves L'Hopital's Rule and any hints and/or explanations would be much appreciated.. If x and y are both positive, evaluate the limit as p approaches 0 of (ln(.1x^p + .9y^p))/p

Answer 1

Differential of the denominator 'p' is 1. Therefore, the answer is the differential of the numerator. Using the chain rule, the differential of the ln function is 1/(.1x^p+.9y^p) and the differential of the power functions is (.1x^p times ln x + .9y^p times ln y) since both x and y are positive constants.

Answer 2

Awesome thank you! I kept mistaking x and y for the variable not p.. Thanks :)