MATH 19A Study Guide - Final Guide: Quotient Rule, Product Rule, Great Circle
Document Summary
Yusuf g oren: evaluating the limits (a) we should balance both the numerator and the denominator to match the arguments. More precisely, since the argument of the sine in the numerator is 3x we need to divide and multiply by 3x. Similarly, we need to multiply and divide by 5x to match the sine in the denominator. Rearranging all the terms we have lim x 0 sin 3x sin 5x. Here, the last equality follows from lim h 0 sin 3x. Alternatively, you can use l"hopital"s rule to get lim x 0 sin 3x sin 5x. 5 where the last equality follows by simply evaluating the last expression. (b) we have x3. Since 1 6 cos x 6 1, by the squeezing theorem, we get lim x x3 lim x . 1 + x3 + cos x cos x cos x x3 = 0.
