MATH 180 Study Guide - Final Guide: Maxima And Minima, Asymptote, Power Rule
Document Summary
Problem 1 solution: for each of the following limits, determine whether the limit exists and, if so, evaluate it. (a) lim x 0 (b) lim x 1 (c) lim x 1. Solution: (a) upon substituting x = 0 into the function f (x) = X2 + 1 1 x we nd that. We can resolve the indeterminacy by multiplying f (x) by the. X2 + 1 1 (x2 + 1) 1 x( x2 + 1 + 1) x. X2 + 1 1 x lim x 0. = 0 (b) when substituting x = 1 into the function f (x) = |(x 1)3| x 1 we nd that. |(x 1)3| x 1 lim x 1+ (x 1)3 x 1 x 1 (x 1)2. Thus, since the one-sided limits are equal to each other, we know that the limit exists and that: lim x 1.
