2-14 - Announcements Reading for this Week 7.8 8.1 and 8.3...

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February 14, 2005 Announcements Reading for this Week: § 7.8, § 8.1 and § 8.3. Midterm # 2 is next week! Thursday, February 24th (Covers § 7.1 - 8.1) Start doing practice Midterms. Modification to Week 8 homework: Problems 1, 5, 7, 11, 12 and 15 in § 8.3 are NOT part of the assigned homework. Today Brief review of L’Hospital’s rule. § 7.8 Improper Integrals: How do you compute the area of unbounded regions? 1
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L’Hospital’s rule Suppose that f and g are differentiable and that g ( x ) = 0 near 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 words we have an indeterminate form of the type 0 0 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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Definition of Improper Integral, Type I 1. If t a f ( x ) dx exists for every t a , then a f ( x ) dx = lim t →∞ t a f ( x ) dx, provided this limit exists (as a finite num- ber) 2. If b t f ( x ) dx exists for every t b , then
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