10121FinalExamSample

10121FinalExamSample - the definite integral to find the...

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NAME: _______________________________ Math 121 Final Exam Sample Spring 2010 Instructions: Answer the multiple choice questions by circling the answers. Answer the free response in the space provided. TRUE OR FALSE: ( 3 pts each) Mark the following statements with “True” or “False” 1. lim x →∞ 2 x 3 + 5 4 x 3 + 1 = 1 2 . T F 2. Suppose f (2) = 1 and f ( x ) 0 2 dx = 5 , then f (0) = 4 . T F 3. If f ( a ) = 0 and f ( a ) > 0 then f ( x ) has a local minimum at x = a . T F 4. Given ln f ( x ) = x 4 , the percentage rate of change of f ( x ) at x = 1 is 25% T F 5. d dx ln x x 2 = 1 x 2 x = 1 2 x 2 . T F FREE RESPONSE: 1. (8 pts) (a) The graph of f ( x ) is shown below. Find f ( x ) dx 0 4 . (b) The graph of f ( x ) = x 2 + x and g ( x ) = x + 1 is shown below. Set up
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Unformatted text preview: the definite integral to find the area between the curves. 2. (6 pts) Suppose a population at time t is given by P ( t ) = P e kt . In the first 5 years the population grew from 20 million to 80 million. Find the population after 8 years. 3. ( 8 pts) Use the logarithm d ifferentiation technique to find the derivative of f ( x ) = (2 x − 1) 5 4 x + 9 ( x 3 + 1) 2 . 4. (5 pts) Given f ( x ) = (2 x + 5) 8 and g ( x ) = e − x . Find d dx f ( g ( x )) . 5. (8 pts) Given f ( x ) = e 2 x + π x . Find f ( x ) ∫ dx and the average value of f ( x ) over the interval [1,3] ....
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10121FinalExamSample - the definite integral to find the...

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