131f09x2 - 3 5. Calculate: d dx [ sin(tan( x 2 / 3 ) ] = 6....

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DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131, Fall 2009, Exam 2 Your Name: No notes or calculators are permitted on this exam. For questions #1-8, do not simplify your answers. But do use enough parentheses to show clearly how expressions are grouped together. For example write ( x - 1)( x - 2) instead of x + 2 · x - 1. Do all work in the exam booklet and show all necessary steps for full-credit. Turn off all cellphones, iPods, alarms, etc. Be prepared to show your UMass ID card when you turn in the exam 1: (10 points) 2: (10 points) 3: (10 points) 4: (10 points) 5: (10 points) 6: (10 points) 7: (10 points) 8: (10 points) 9: (10 points) 10: (10 points) TOTAL: (100) 1
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1. Calculate: d dx ( 6 x + 5 x - x 4 ) = 2. Calculate: d dx [ e - x cos( x 3 + 1) ] = 2
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3. Let f ( x ) = ln(3 x - 1). Calculate f 00 ( x ). 4. Calculate: d dx ( (4 x 2 - 1) 2 / 5 1 + sin 2 x ) =
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Unformatted text preview: 3 5. Calculate: d dx [ sin(tan( x 2 / 3 ) ] = 6. Calculate f ( z ) where: f ( z ) = ( z 3 + 1 z + cos 2 z ) 2010 4 7. Calculate: d dx [ 2 + arctan(4 x ) ] = 8. Let y satisfy the equation x 2 e y = y 3-1. Then dy dx = 5 9. Find the equation of the tangent line to the curve y = x √ 8-x at the point (4 , 8). 6 10. Let f ( x ) = 2 x 3 + 2 x + 1. Let g ( x ) be the inverse function of f ( x ). This means that f ( g ( x )) = x and g ( f ( x )) = x. (a) Notice that f (-1) =-3 and f (0) = 1 and f (1) = 5. What is g (5)? (2 points) (b) Calculate f ( x ). (3 points) (c) Take the derivative of both sides of f ( g ( x )) = x with respect to x . Now plug in x = 5. Use this to determine g (5). (5 points) 7 This page is for scratchwork 8...
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This note was uploaded on 11/22/2011 for the course MATH 131 taught by Professor Hall-seelig during the Fall '08 term at UMass (Amherst).

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131f09x2 - 3 5. Calculate: d dx [ sin(tan( x 2 / 3 ) ] = 6....

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