Chapter 2 Section 3

# Chapter 2 Section 3 - We can use the facts lim x c x = c...

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Chapter 2 Section 3 Calculating limits using limit laws

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Objectives: Compute limits using limit laws.
The limit laws state that if lim x c f(x) and lim x c g(x) both exist, then ( proofs are on page A18 of the appendix ) 1. lim x c (f(x) + g(x)) = lim x c f(x) + lim x c g(x) 2. lim x c kf(x) = klim x c f(x) 3. lim x c (f(x)·g(x)) = lim x c f(x)·lim x c g(x) 4. If lim x c g(x) h 0, then ) ( lim ) ( lim ) ( ) ( lim x g x f x g x f c x c x c x =

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In words, 1. The limit of a sum is the sum of the limits. 2. The limit of a constant times a function is the constant times the limit of the function. 3. The limit of a product is the product of the limits. 4. The limit of a quotient is the quotient of the limits.

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Unformatted text preview: We can use the facts lim x c x = c and lim x c k = k and the previous limit laws to evaluate some simple limits. Examples: page 82 1 14 3 lim . 16 ) 9 3 )( 1 ( lim . 14 14 lim . 4 lim . 2 4 2 2 3 3 +--+ → →-→-→ t t x x x t x x x Examples: page 82 x x 3 lim . 2-→ Examples: page 82 14 lim . 4 3-→ x Examples: page 82 ) 9 3 )( 1 ( lim . 14 2 2-+ → x x x Examples: page 82 1 14 3 lim . 16 4 +-→ t t t 9-3g(x) 1 f(x) lim 28. 3g(x)) (2f(x) lim 26. : following the find 1, g(x) lim and 3 f(x) lim that Assuming 4-x 4-x 4-x 4-x + + = = → → → →...
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## This note was uploaded on 09/28/2009 for the course MATH 1550 taught by Professor Wei during the Spring '08 term at LSU.

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Chapter 2 Section 3 - We can use the facts lim x c x = c...

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