Math 30 - Final-version 2

Math 30 - Final-version 2 - San Jose State University Math...

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San Jose State University Math 30 - Fall 09 Final Exam Show Your Work Simplify Your Answers Name:
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Problem 1: If f ( x ) = x - 3, g ( x ) = x 2 , and h ( x ) = x 3 + 2, find f g h ( x ). Solution : Problem 2: Evaluate lim x →- 4 x 2 + 5 x + 4 x 2 + 3 x - 4 , if it exists. Solution :
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Problem 3: Find lim u →∞ 4 u 4 + 5 ( u 2 - 2)(2 u 2 - 1) . Solution : Problem 4: Find the derivative of g ( x ) = cosh(ln x ). Solution :
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Problem 5: Differentiate f ( x ) = x + 1 3 x 2 . Solution : Problem 6: Find f 0 ( x ) and f 00 ( x ), for f ( x ) = x 4 e x . Solution :
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Problem 7: Differentiate f ( x ) = sin 2 ( e sin 2 x ). Solution : Problem 8: Find the derivative of f ( t ) = tan( e t ) + e tan t . Solution :
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Problem 9: Find dy/dx given that x 2 y 2 + x sin y = 4. Solution : Problem 10: Differentiate y = ( x ) x . Solution :
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Problem 11: A ladder 15 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 5 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 10 ft from the wall? Solution : Problem 12: Find the linearization L ( x ) of the function f ( x ) = x + 3 at a = 1. Use L ( x ) to approximate the number 3 . 98. Solution :
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Problem 13: Let f ( x ) = 2 + 3 x - x 3 . (a) Find the local maximum and minimum values of
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