# L25 - L25 Indeterminate Forms and LHpitals Rule o ex 1 , x...

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L25 – Indeterminate Forms and L’Hˆopital’s Rule Consider F ( x ) = e x - 1 x , x 6 = 0. Find lim x 0 e x - 1 x Find lim x →∞ ln( x ) x 1

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L’Hˆopital’s Rule – Suppose that f and g are diﬀerentiable and g 0 ( x ) 6 = 0 near a (except possibly at a ). Suppose that and or and then if it exists or is ±∞ . Note: 1. 2. 3. 2
Find lim x 0 e x - 1 x Find lim x 0 e x - 1 x 3 Find lim x 0 - tan( x ) x 2 3

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Find lim x 0 sec( x ) - 1 x 2 Find lim x π + sin( x ) x - π 4
Find lim x 0 + ln( x ) csc( x ) 5

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Indeterminate Products If lim x a f ( x ) = 0 and lim x a g ( x ) = ±∞ , then lim x a f ( x ) g ( x ) = Rewrite as Find lim x 0 + x ln( x ) = 6
Find: lim x π 4 (1 - tan( x ))sec(2 x

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## This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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L25 - L25 Indeterminate Forms and LHpitals Rule o ex 1 , x...

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