Math 1351 011 Exam III A November 10 2006 Answer the problems on separate paper You do not need to rewrite the problem statements on your answer sheets Do your own work Show all relevant steps which lead to your solutions Attach this question sheet to the front of your answer sheets 1 Consider the function y 2x 1 a 9 pts Construct a linearization for the function at x 4 b 6 pts Use the linearization constructed in part a to construct an approximation for the value of 2 3 8 8 12 pts Using calculus find the absolute maximum and absolute minimum values of f x 3 x 4 4 x 3 12 x 2 1 on the interval 2 1 3x 1 Find and identify each of the following if they exist record 2 x 1 2 your solutions to parts a through m on the back of this page 45 pts Let f x a b c d e f g h i j k l m domain of f intercepts of f vertical asymptotes to the graph of f horizontal asymptotes to the graph of f critical numbers of f intervals on which the graph of f is increasing intervals on which the graph of f is decreasing local maximum points of the graph of f local minimum points of the graph of f 2nd order critical numbers of f intervals on which the graph of f is concave up intervals on which the graph of f is concave down inflection points of the graph of f Then incorporate all of the above information into a sketch the graph of f 4 30 pts Find the following limits if they exist 2 a lim x 2 x 2 x 2 x 2 4 x 1 d lim x 2 ln x x 0 1 cos x x 0 sin 2 x b lim e lim x 1 x x c lim x 0 x sin x x cos x Solution Space for Problem 3 Problem Statement a domain of f b intercepts of f c vertical asymptotes to the graph of f d horizontal asymptotes to the graph of f e critical numbers of f f intervals on which the graph of f is increasing g intervals on which the graph of f is decreasing h local maximum points of the graph of f i local minimum points of the graph of f j 2nd order critical numbers of f k intervals on which the graph of f is concave up l intervals on which the graph of f is concave down m inflection points of the graph of f Problem Solution
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