1007Test3_09sol

# 1007Test3_09sol - Test 3 Wednesday March 4 2009 MATH 1007G...

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Test 3, Wednesday March 4, 2009 MATH 1007G Last Name :_________________ First Name:_______________ ID #:____________________ Total marks:36 Total time: 50 minutes No Calculators are allowed. Show your work. Question 1. Differentiate the following functions. (DO NOT simplify your results) a) [3] f x x x ( ) tan = - 2 f x x x x x ' ( ) .( tan ) .( sec ) ( tan ) = - - - - 1 2 2 2 2 b) [3] f x x x x x x ( ) ( ) / / = + = + 3 2 3 5 6 2 2 f x x ( ) . / = + - 1 2 5 6 5 6 1 c) [3.5] f x x x x e x ( ) ( )(cos ) = + - 3 f x x x e x x x e x x ' ( ) ( )(cos ) ( )( sin ) = + - + + - - 3 1 2 3 Question 2. [3] At which point on the curve y e x x = + - 1 4 5 , is the tangent line parallel to the line y x - + = 7 2 0 ? The slope of the tangent line to the curve y e x x = + - 1 4 5 at x is dy dx e x = - 4 5 . The slope of the tangent line to the curve y x y x - + = = - 7 2 0 7 2 at x is 7 . So the lines will be parallel when the slope are same i.e. y

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1007Test3_09sol - Test 3 Wednesday March 4 2009 MATH 1007G...

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