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Unformatted text preview: Lecture 34 18.01 Fall 2006 Lecture 34: Indeterminate Forms- LHpitals Rule LHpitals Rule (Two correct spellings: LHpital and LHospital) Sometimes, we run into indeterminate forms. These are things like and For instance, how do you deal with the following? lim x 3- 1 = ?? x 1 x 2- 1 Example 0. One way of dealing with this is to use algebra to simplify things: lim x 3- 1 = lim ( x- 1)( x 2 + x + 1) = lim x 2 + x + 1 = 3 x 1 x 2- 1 x 1 ( x- 1)( x + 1) x 1 x + 1 2 In general, when f ( a ) = g ( a ) = 0 , f ( x ) f ( x ) x lim a f ( x )- f ( a ) f ( a ) lim = lim x- a = x- a = x a g ( x ) x a g ( x ) lim g ( x )- g ( a ) g ( a ) x a x- a x- a This is the easy version of LHpitals rule: f ( x ) f ( a ) lim = x a g ( x ) g ( a ) Note: this only works when g ( a ) = 0 ! In example 0, f ( x ) = x 3 = 1; g ( x ) = x 2- 1 f ( x ) = 3 x 2 ; g ( x ) = 2 x = f (1) = 3; g (1) = 2 The limit is f (1) /g (1) = 3 / 2 . Now, lets go on to the full LHpital rule....
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This note was uploaded on 02/27/2009 for the course MATH 155b taught by Professor Staff during the Fall '08 term at Vanderbilt.
- Fall '08