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MTH132-Quiz2-Solutions (2) - Page 1 Name(Print Clearly...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: MTH132 Section 5 & 18, Quiz 2 Sept 26, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 15 minutes. 1 [2 pts each] . Find the following derivatives (a) ) ( 2 x dx d . 2 x = (b) ) sin 3 ( x dx d . cos 3 x = (c) ) sin 3 ( 2 x x dx d use product rule ( f = 3sinx , g =x^2) x x x x 2 sin 3 cos 3 2 + = (d) ) sin 3 ( 2 x x dx d use quotient rule ( f = 3sinx , g =x^2) 4 2 2 sin 3 cos 3 x x x x x - = (e) ) (cos 999 999 x dx d Recall x dx d x dx d k k k n k n cos cos 4 4 = + + [Ex 3.4 Page 189 #49] 3 249 4 999 + × = , so 3 = k x x x x x dx d x dx d sin ) cos ( ) sin ( cos ) (cos ) (cos 3 3 999 999 = - = - = = =
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Page 2 10/18/2011 2 [4 pts each] . If x x x f 9 ) ( + = , find an equation for the tangent line when . 3 - = x [Page 156 #13] (a) Find the derivative of ). ( x f 2 1 9 1 ) 9 ( - - - = + = x x x f (b) Use point-slope equation to describe the tangent line ) ( 0 0 x x m y y - = - , 6 3 / 9 3 ) 3 ( ) ( , 3 0 0 0 - = - + - = - = = - = f x f y x The slope of the tangent line at this point: 0 1 1 ) 3 ( 9 1 ) 3 ( 2 = - = - - = - = f m So the tangent line is: )) 3 ( ( 0 ) 6 ( - - × = - - x y 0 6 = + y 3 [6 pts] . Suppose x x f cos ) ( = . (a) Use the definition of derivative to express the derivative of
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