13112an2.7-9

13112an2.7-9 - c Kendra Kilmer January 11, 2012 Section 2.3...

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c c Kendra Kilmer January 11, 2012 Section 2.3 Calculating Limits Using the Limit Laws Limits Laws Let f and g be two functions, and assume that lim x a f ( x ) = L lim x a g ( x ) = M where L and M are real numbers (both limits exist). Then 1. lim x a k = k for any constant k 2. lim x a x = a 3. lim x a [ f ( x ) + g ( x )] = lim x a f ( x ) + lim x a g ( x ) = L + M 4. lim x a [ f ( x ) g ( x )] = lim x a f ( x ) lim x a g ( x ) = L M 5. lim x a k f ( x ) = k lim x a f ( x ) = kL for any constant k 6. lim x a [ f ( x ) · g ( x )] = [ lim x a f ( x )][ lim x a g ( x )] = LM 7. lim x a f ( x ) g ( x ) = lim x a f ( x ) lim x a g ( x ) = L M if M n = 0 8. lim x a [ f ( x )] n = b lim x a f ( x ) B n where n is a postive integer 9. lim x a n r f ( x ) = n R lim x a f ( x ) = n L , L > 0 for n even Example 1: Determine the following limits: a) lim x 2 10 b) lim x 3 x 2 + 3 x 2 c) lim x 3 3 x + 2 x 4 Limits of Polynomial and Rational Functions 1. lim x a f ( x ) = f ( a ) , f any polynomial function 2. lim x a r ( x ) = r ( a ) , r any rational function with nonzero denominator at x = a 7
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c c Kendra Kilmer January 11, 2012 Example 2: Find each limit. a) lim
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13112an2.7-9 - c Kendra Kilmer January 11, 2012 Section 2.3...

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