Math 1351 013 Exam IV A April 16 2004 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 Let a b c d e f g h i j k f x 3 4x x2 2 Find and identify each of the following if they exist domain of f intercepts of f local maximum points of the graph of f local minimum points of the graph of f intervals on which the graph of f is increasing intervals on which the graph of f is decreasing 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 vertical asymptotes to the graph of f horizontal asymptotes to the graph of f Then incorporating all of the above information into a sketch the graph of f 2 Do four 4 of the following Find the following limits if they exist 2 x 5 x 4 x 5 x 4 2 x 1 a lim c lim sin x 2 sin 2 x lim 1 1 sin3 x 3 x e x 0 x 0 x cos x x cos x b lim d lim x 2 sin x 0 x 0 1 x2 3 Find the area the largest rectangle with base on the x axis which can be inscribed inside the triangle with vertices 6 0 6 0 0 3 See picture 4 Westel Corporation manufactures telephones and has developed a new cellular phone Production analysis show that its price must not be set at less than 50 Also if x units are sold then the optimal price is given by the formula p x 150 x The total cost for producing x units is given by the formula C x 2500 30 x Find the maximum profit and determine the price that should be charge to achieve that profit 5 Do four 4 of the following Find the following indefinite integrals a 6 7 x dx b x 1 x e 1 3 dx 2 3x dx 2 b dx cos 2 x d x 4 4 1 x 2 dx
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