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Unformatted text preview: 1 + F ( x ). lim x → 1 + x 2 − 1  x − 1  = lim x → 1 + x 2 − 1 x − 1 = lim x → 1 + ( x − 1)( x + 1) x − 1 = lim x → 1 + ( x + 1) = 2. b) Find lim x → 1F ( x ). lim x → 1x 2 − 1  x − 1  = lim x → 1x 2 − 1 − ( x − 1) = lim x → 1( x − 1)( x + 1) − ( x − 1) = lim x → 1− ( x + 1) = − 2 . . c) Does lim x → 1 F ( x ) exist? Answer: No Justify your answer: lim x → 1 + F ( x ) ± = lim x → 1F ( x ) = ⇒ The limit at 1 does not exist. Question 4. Consider the function f ( x ) = 3 x . Use the de±nition of the derivative to compute f ± (3). Answer: f ± (3) = lim h → f (3 + h ) − f (3) h = lim h → 3 3+ h − 1 h = lim h → 3 − (3+ h ) 3+ h h = lim h → − h h (3 + h ) = lim h → − 1 3 + h = − 1 3 . 2...
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 Fall '08
 DUMITRISCU
 Calculus, Limit, lim F

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