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calculusch7[1].8

# calculusch7[1].8 - 7.7 Indeterminate forms and...

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Unformatted text preview: 7.7 Indeterminate forms and L’Hospital’s Rule If we have a limit of the form lim x → a f ( x ) g ( x ) where both f ( x ) → 0 and g ( x ) → 0 as x → a , then this limit may or may not exist and is called an indeterminate form of type . If we have a limit of the form lim x → a f ( x ) g ( x ) where both f ( x ) → ∞ (or-∞ ) and g ( x ) → ∞ (or-∞ ) as x → a , then this limit may or may not exist and is called an indeterminate form of type ∞ ∞ . Definition 1 (L’Hospital’s Rule) . Suppose f and g are differentiable and g ( x ) 6 = 0 on an open interval I that contains a (except possibly at a ). Suppose that lim x → a f ( x ) = 0 and lim x → a g ( x ) = 0 or that lim x → a f ( x ) = ±∞ and lim x → a g ( x ) = ±∞ (In other word, we have an indeterminate form of type or ∞ ∞ .) Then lim x → a f ( x ) g ( x ) = lim x → a f ( x ) g ( x ) if the limit on the right side exists (or is ∞ or-∞ )....
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calculusch7[1].8 - 7.7 Indeterminate forms and...

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