Two Somewhat Similar Problems
Date: Mon, 9 Jan 1995 09:11:29 -0500 (EST) From: Secret Someone Okay, last two (for now): 1. Evaluate: lim Integral from 1 to 1+h of (x^5+8)^.5 dx all over h h->0 UGH!!@$@#$@%#! 2. If F is differentiable for all x then evaluate lim Integral from a to a+h of F'(x) dx all over h h->0 These two problems seem somewhat similar. (in appearance and in the fact that I can't do either one of them) Thanks for the help, Burris
Date: 9 Jan 1995 23:43:20 -0500 From: Dr. Ken Subject: Re: your mail Hello there! Yes, you're right, these two problems are _very_ similar. Do you know L'Hopital's rule? Do you know any other word with two apostrophes in it? I sure don't. Anyway, notice that in these limits, the numerators and denominators are both going to zero. That means we can use L'Hopital's rule, and take the derivative with respect to h of the top and the bottom. So just remember that the derivative of the integral from c to x of f(u) du is f(x), where c is constant and x is a variable. That should be enough to get you through these problems. Yup, it was a trick. -Ken "Dr." Math
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