math102_1999 - The University of British Columbia Sessional...

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The University of British Columbia Sessional Examinations – December 1999 Mathematics 102 Sections 101, 102, 104, 105 and 107: Keshet, Li and Sjerve Closed book examination Time: 2 ½ hours Special Instructions: Calculators are allowed. Show your work in the spaces provided. You must justify all your work to receive full credit. 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total 100
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Marks [10] 1. Find the derivatives of the following functions. DO NOT TRY TO SIMPLIFY. a) f (x) = tan(1/ x ). b) f (x) = sin( e x ). c) f (x) = (1+ cos( x )) 1/3 d) f (x) = 1 ln + x x . ________________________________________________________________________
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[10] 2. Shown below is the graph of a function y = f’ ( x ). a) Sketch the graph of the function f" ( x ). b) Sketch the graph of the function f ( x ) that satisfies f (0) = 0. ________________________________________________________________________
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[10] 3. a) Define the derivative f ( x ) of a function f ( x ). b) Using only the definition of the derivative, find f ( x ) for the function f ( x ) = 1/ x . No marks will be given if you only use the rules of differentiation. [10] 4. A bird gains energy from food it gathers by foraging, but the task of foraging also consumes energy.
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math102_1999 - The University of British Columbia Sessional...

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