Expert: Sherry Wallin - 10/22/2009

Question
how would you solve this derivative    Lim [cos(3.14/2+h) - cos(3.14/2)]/h as h aprroaches 0

Answer
Was the problem given this way or did you put in 3.14 for pi? And in the denominator of the first term is it 2 or 2+h? If it is 2+h you need to write lim(h->0)[cos(3.14/(2+h))-cos(3.14/2)]/h. This is called an indeterminate form of 0/0 when you plug in 0 for h so you get to use L'Hositals Rule which says if the derivative exists around the point but not necessarily at the point then the lim(h->0) of the function is the same as the lim of the derivative. The derivative of cos(3.14/(2+h)) = -sin(3.14/(2+h)) and as h approaches 0 it is -1*1=-1. the derivative of -cos(3.14/2) is 0 since -cos(3.14/2) is a constant and the derivative of h in the denominator is 1 so the answer is -1.

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