Final Exam&solutions

Final Exam&solutions - San Jose State University Math...

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San Jose State University Math 30P - Spring 09 Final Exam With Solutions Show Your Work Simplify Your Answers Name:

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Problem 1: If f ( x ) = x 2 - 1, ﬁnd f f . Solution : x 4 - 2 x 2 Problem 2: What is the domain of f ( x ) = 1 x + 2 - ln( x + 1)? Solution : ( - 1 , )
Problem 3: If f ( x ) = sinh( x ), g ( x ) = ln( x + 1), and h ( x ) = x 2 , ﬁnd ( f g h )( x ). Solution : sinh(ln( x 2 + 1)). Problem 4: Suppose f ( x ) = 1 + e sinh( x ) . Find f - 1 ( x ). Solution : f - 1 ( x ) = sinh - 1 (ln( x - 1))

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Problem 5: Solve the equation ln(sinh - 1 ( x )) = 1 for x . (Just give the formula for x , you don’t need your calculator.) Solution : x = sinh( e ) Problem 6: Evaluate lim x 3 - x + 1 x - 3 . Solution : -∞
Problem 7: Evaluate lim x →∞ 3 x x 2 + 2 x + 1 . Solution : 0 Problem 8: Evaluate lim x 1 e 1+ t sin ± π 2 t ² using continuity. Solution : e 2

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Problem 9: Using the deﬁnition of derivative, calculate the derivative of f ( x ) = 3 x + 19. (You must show your work to get credit.)
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Final Exam&solutions - San Jose State University Math...

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