06FLHopital - Indeterminate Forms - LHpitals Rule o At x =...

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Indeterminate Forms - L’Hˆopital’s Rule At x = u , has the indeterminate form if lim x u f ( x )= and lim x u g ( x (1) f ( x ) g ( x ) 0 0 00 (2) f ( x ) g ( x ) ∞∞ (3) f ( x ) · g ( x )0 ·∞ 0 (4) f ( x ) - g ( x ) ∞-∞ (5) [ f ( x )] g ( x ) 0 0 (6) [ f ( x )] g ( x ) 0 0 (7) [ f ( x )] g ( x ) 1 1 HERE: u stands for any of the symbols a , a - , a + , -∞ ,+ . L’Hˆopital’s Rule (1) and (2) If: f ( x ) g ( x ) has the interdeterminate form 0 0 or at u and lim x u f 0 ( x ) g 0 ( x ) exists (i.e. this limit is a finite number or -∞ or ) then lim x u f ( x ) g ( x ) = lim x u f 0 ( x ) g 0 ( x ) . (3) If f ( x ) · g ( x ) has the interdeterminate form 0 at u , then rewrite: f ( x ) · g ( x f ( x ) 1 /g ( x ) , which has the interdeterminate form 0 0 at u or f ( x ) · g ( x g ( x ) 1 /f ( x ) , which has the interdeterminate form at u and then apply L’Hˆ opital’s Rule. 1
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(4) If f ( x ) - g ( x ) has the interdeterminate form ∞-∞ at u , then use algebraic manipulation to convert f ( x ) - g ( x ) into a form of the type 0 0 or and then apply L’Hˆ opital’s Rule. (5) If [ f ( x )] g ( x ) has the interdeterminate form 0 0 at u , then follow these steps:
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This note was uploaded on 12/13/2011 for the course MATH 142 taught by Professor Kustin during the Fall '11 term at South Carolina.

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06FLHopital - Indeterminate Forms - LHpitals Rule o At x =...

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