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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 +14 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 2f ( x ) = lim x 2x 2 1= 3 lim x 2 + f ( x ) = lim x 2 + x + n = 2 + n For the limit to exist lim x 2f ( x ) = lim x 2 + f ( x ) so 3 = 2 + n means that n =1 Now lets check the function value at that pointâ€¦ 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.
 Spring '08
 Johnson
 Calculus, Logic, Rate Of Change

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