quizsoln5 - lim D x f ( x + D x ) -f ( x ) D x = lim D x 4(...

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Name:___________________________ Math 155 Quiz 5 26 September 2006 Instructions : This quiz is closed book and closed notes. You may use a calculator. Label your answers and show all work. 1. (4 pts) Find the average rate of change of f ( x ) = 5 x 2 near x =1 as a function of x and find the limit as x 0 . Average Rate of Change f (1+ D x ) - f (1) D x = 5(1+ D x ) 2 - 5(1) 2 D x = 5 +10D x + 5D x 2 - 5 D x =10 + 5D x 2. (6 pts) Let f ( x ) = x 2 x < 2 x + 2 x > 2 2 x = 2 (a) Find lim x 2 - f ( x ) = 4 (b) Find lim x 2 + f ( x ) = 4 (c) Find lim x 2 f ( x ) = 4 (d) Find f (2) = 2 (e) Is f ( x ) continuous at x = 2 ? Why or why not? No, because lim x 2 f ( x ) f (2) Extra Credit 1 Instantaneous Rate of Change lim D x 0 (10 + 5D x ) =10
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Unformatted text preview: lim D x f ( x + D x ) -f ( x ) D x = lim D x 4( x + D x ) 2 +1-4 x 2 +1 ( ) D x = lim D x 4 x 2 + 8 x D x + 4D x 2- 4 x 2- 1 D x = lim D x D x (8 x + 4D x ) D x = lim D x 8 x + 4D x = 8 x Thus, the derivative f '( x ) = 8 x Extra Credit 2 lim x 2-f ( x ) = lim x 2-x 2- 1= 3 lim x 2 + f ( x ) = lim x 2 + x + n = 2 + n For the limit to exist lim x 2-f ( x ) = lim x 2 + f ( x ) so 3 = 2 + n means that n =1 Now lets check the function value at that point… f (2) = 3 so lim x 2 f ( x ) = f (2) and the function is continuous...
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This note was uploaded on 02/21/2008 for the course MATH 155 taught by Professor Johnson during the Spring '08 term at Colorado State.

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quizsoln5 - lim D x f ( x + D x ) -f ( x ) D x = lim D x 4(...

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