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Math 30 - Final-version 2 with solns

# Math 30 - Final-version 2 with solns - San Jose State...

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San Jose State University Math 30 - Fall 09 Final Exam with Solutions 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 : x 6 + 4 x 3 + 1 Problem 2: Evaluate lim x →- 4 x 2 + 5 x + 4 x 2 + 3 x - 4 , if it exists. Solution : 3/5
Problem 3: Find lim u →∞ 4 u 4 + 5 ( u 2 - 2)(2 u 2 - 1) . Solution : 2 Problem 4: Find the derivative of g ( x ) = cosh(ln x ). Solution : 1 x sinh(ln x )

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Problem 5: Differentiate f ( x ) = x + 1 3 x 2 . Solution : 2( x 1 / 2 + x - 1 / 3 )(1 / 2 · x - 1 / 2 - 1 / 3 · x - 4 / 3 ) = 1+1 / 3 · x - 5 / 6 - 2 / 3 · x - 5 / 3 Problem 6: Find f 0 ( x ) and f 00 ( x ), for f ( x ) = x 4 e x . Solution : f 0 ( x ) = e x ( x 4 + 4 x 3 ); f 00 ( x ) = e x ( x 4 + 8 x 3 + 12 x 2 )
Problem 7: Differentiate f ( x ) = sin 2 ( e sin 2 x ). Solution : 4 sin x · cos x · e sin 2 x · sin( e sin 2 x ) · cos( e sin 2 x ) Problem 8: Find the derivative of f ( t ) = tan( e t ) + e tan t . Solution : e t sec 2 ( e t ) + sec 2 te tan t

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Problem 9: Find dy/dx given that x 2 y 2 + x sin y = 4. Solution : dy/dx = - sin y + 2 xy 2 2 yx 2 + x cos y Problem 10: Differentiate y = ( x ) x .
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Math 30 - Final-version 2 with solns - San Jose State...

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