1.6 Calculating Limits Using the Limit Laws

# 1.6 Calculating Limits Using the Limit Laws - the...

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Calculating Limits Using the Limit Laws Section 1.6

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Limit Laws
Some Basic Limits Let a and c be real numbers and let n be a positive integer. b b c x = lim c x c x = lim n n c x c x = lim

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The Limit of a Function Involving a Radical Let n be a positive integer. The following limit is valid for all c if n is odd, and is valid for c > 0 if n is even. n n c x c x = lim
Thm: One-sided and 2-Sided Limits A function f(x) has a limit as x approaches c iff the right-hand and left-hand limits at c exist and are equal lim ( ) lim ( ) lim ( ) x c x c x c If f x L and f x L then f x L + - = = =

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Limits of Trig. Functions Let c be a real number in the domain of the given trig. function. 1. 2. 3. c x c x sin sin lim = c x c x cos cos lim = c x c x tan tan lim =
4. 5. 6. c x c x cot cot lim = c x c x sec sec lim = c x c x csc csc lim =

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A Strategy for Finding Limits 1. Use direct substitution if possible. 2. See if you can factor the numerator so that

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Unformatted text preview: the denominator will cancel.(tiny hole in graph) 3. Use a graph or table to reinforce conclusion 4. If direct substitution produces the indeterminate form try cancellation or rationalization techniques to rewrite the denominator so that it doesn’t have 0 as its limit. Theorem The Squeeze Theorem If h(x) < f(x) < g(x) for all x in an open interval containing c, except possibly at c itself, and if then exists and = L. ) ( lim ) ( lim x g L x h c x c x → → = = ) ( lim x f c x → Special Trigonometric Limits 1. 2. 1 sin lim = → x x x cos 1 lim =-→ x x x Joke Time v Why do ducks have flat feet? v To stamp out forest fires Why do elephants have flat feet? To stamp out burning ducks...
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1.6 Calculating Limits Using the Limit Laws - the...

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