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Unformatted text preview: x 2(2x ) + x = lim x 2 + (2x )(2 + x )(2x ) + x = lim x 2 + 2 + x1 + x =2 b) Find lim x 2F ( x ). lim x 24x 2  2x  +  x  = lim x 24x 2 2x + x = lim x 2(2x )(2 + x ) 2x + x = lim x 22 + x + x = 6 c) Does lim x 2 F ( x ) exist? Answer: No Justify your answer: lim x 2 + F ( x ) 6 = lim x 2F ( x ) = The limit at 2 does not exist. Question 4. Consider the function f ( x ) = 2011 x 2 . Use the denition of the derivative to compute f (2). Answer: f (2) = lim h f (2 + h )f (2) h = lim h 2011 (2+ h ) 22011 2 2 h = lim h 2011 { 2 2(2 + h ) 2 } h 2 2 (2 + h ) 2 = lim h 2011(22h )(2 + 2 + h ) h 2 2 (2 + h ) 2 = lim h 2011(1)(4 + h ) 2 2 (2 + h ) 2 =2011 4 . 2...
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This note was uploaded on 12/19/2011 for the course MAT 1330 taught by Professor Dumitriscu during the Fall '08 term at University of Ottawa.
 Fall '08
 DUMITRISCU
 Calculus

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