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Unformatted text preview: 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 ILimits 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 sin lim b. x x x 2 2 lim + c. 2 2 1 1 lim 2 x x x d. x x x 3 sin 2 lim e. ) 1 2 (ln lim 3 2 + + x x e x f. 1 1 lim 2 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) < + = , 1 ), 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 Part IIDerivatives and Applications of Derivatives 5. Use the definition of derivative to find f(x) for each of the following: (Section 3.1) a. 2 3 ) ( 2 + = x x x f b. x x f = 3 ) ( c. 1 2 ) ( + = x x f 6. Find dx dy for each of the following: (Sections 3.2 3.6) a) x x y 2 tan 3 = b) 3 cos x y = c) 1 cos = y x d) 3 2 5 3 2 + = x x x y e) x x y 2 ) 1 ( + = f) 2 arcsin t y = g) x e y x arctan = h) ) tan(arcsin t y = i) ) sec sin( x arc y = j) 4 3 2 1 = x x y k) 2 2 2 14 x x y + = l) ) ln (sin x x e y x + = m) sinx=x(1+tany) x x y 3 cosh sinh 4 3 = (this derivative comes from 5.9) 7. For each of the following, find an equation of the tangent line to the graph of f at the given point. a. ) 4 ( ) ( + = x e x f x ( , ) b . ( ) 2 2 3 1 ) ( x x x f = (4, 1/16) Related Rates (Section 3.7) 8. The edges of a cube are expanding at a rate of 5 centimeters per second. How fast is the surface area of the cube changing when each edge is 4.5 centimeters?...
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This note was uploaded on 01/12/2012 for the course MATH 2554 taught by Professor Pamelasatterfield during the Spring '11 term at NorthWest Arkansas Community College.
- Spring '11