Survey of Calculus Final exam review--Departmental

# Survey of Calculus Final exam review--Departmental - Survey...

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Fall 2005 (Brief Applied Calculus, 3 rd Edition. Berresford, Rockett. Houghton Mifflin, 2004.) All work should be shown and all answers should be exact unless stated otherwise. It is fine to leave radicals in the denominator of a fraction, but they should be reduced. The departmental formula sheet and an acceptable graphing calculator are the only resources allowed for use during the final exam. Each problem on this review sheet is matched with its corresponding objective in the course outline and the section of the textbook in which it appears. [Objective #1, Section 2.1] 1. Evaluate the following limits without using a graphing calculator or making tables. a. ( 29 + - 2 1 25 5 lim t t t b. x x x x x x + - - - 2 2 3 1 6 3 3 lim c. 2 2 1 1 lim 2 - - x x x [Objective #1, Sections 2.1, 2.7] 2. Use the given graph to answer the following: a. ) ( lim 0 x f x + b. ) ( lim 0 x f x - c. ) ( lim 0 x f x d. x-values where the function is discontinuous e. x-values where the function is nondifferentiable f. x-values where the slope of the tangent line is zero. g. x-values where the slope of the tangent line is undefined [Objective #2, Section 2.2] 3. Use the definition of derivative to find ) ( ' x f . a. 2 3 2 ) ( 2 + - = x x x f b. x x f 1 ) ( = [Objective #2, Sections 2.3, 2.4, 2.6] 4. Find the equation for the tangent line to the curve of 2 6 3 ) ( 2 + - = x x x f at the point (0,2). Write your answer in slope-intercept form. 5. Find dx dy for each of the following: a. 4 2 5 1 2 4 3 x x x x y + - - = b. ( 29 1 3 6 3 2 3 4 + = x x y c. ( 29 ( 29 5 2 1 5 3 2 - + - = x x x y d. y= x x x 1 2 3 2 + - e. 1 1 2 + - = x x x y f. 3

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Survey of Calculus Final exam review--Departmental - Survey...

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