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Unformatted text preview: Math 1a LHopitals Rule Fall, 2009 & $ % Indeterminate Forms Were considering lim x a f ( x ) g ( x ) . We begin with several indeterminate forms: Type : lim x a f ( x ) = 0 and lim x a g ( x ) = 0 Type : lim x a f ( x ) = or- and lim x a g ( x ) = or- LH opitals Rule (or LHospitals Rule ) is: if f and g are differentiable and g ( x ) is not zero near a (but g ( a ) may be zero). Then if the limit (on the left, below) is of indeterminate form 0 / 0 or / , then lim x a f ( x ) g ( x ) = lim x a f ( x ) g ( x ) provided the limit on the right exists (or is + or- ). 1 For each of the following, verify that the given limit is in an indeterminate form, then use LH opitals Rule (if possible) to determine the limit. (a) lim x sin( x ) x (b) lim x sin( x ) x 2 (c) lim x + sin( x ) x (d) lim x 1 x 2- 1 ln( x ) (e) lim x e x- 1 x (f) lim x ln( x ) x (g) lim x...
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This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.
- Fall '09