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final exam review f06 - Calculus I Departmental Final Exam...

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Calculus I, Departmental Final Exam Review tv f/06 This review should be used as a guide only. These problems are intended to represent the types of skills that you should have mastered in Calculus I. The final exam will require you to show mastery of these same skills, but through different problems. A successful Calculus student should be able to recognize the problem type and proceed in a methodical manner to a solution rather than memorize how to work a PARTICULAR problem. Part I—Limits and Continuity and Applications 1. Use the given graph to answer questions a – g 2. Evaluate the following limits analytically (do not use a table or a graph). Give exact answers. (Sections 2.3 – 2.4) a. ( ) x e x x π sin lim 0 b. x x x 2 2 lim 0 + c. 2 2 1 1 lim 2 x x x d. x x x 3 sin 2 lim 0 e. ) 1 2 (ln lim 3 2 + + x x e x f. 1 1 lim 2 0 x x x e e g. ) ( lim 1 x f x + where > + = 1 , 1 1 , ) ( 2 x x x x x f h. 2 2 lim 2 x x x i. 3. Find the x-values (if any) at which f is not continuous. Identify any discontinuities as removable or non-removable. (Section 2.4) a) 10 3 2 ) ( 2 + = x x x x f b) < + = 0 , 1 0 ), 1 ln( ) ( 2 x x x x x f 4. Find any vertical asymptotes for a) 1 1 2 + = x x y b) 1 1 2 = x x y
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