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1-3 Evaluating Limits Analytically

1-3 Evaluating Limits Analytically - Evaluating Limits...

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Evaluating Limits Analytically Section 1.3

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Thm. 1.1 Some Basic Limits Let a and c be real numbers and let n be a positive. b b c x = lim c x c x = lim n n c x c x = lim
Thm. 1.2 Properties of Limits Let b and c be real #s, let n be a positive integer, and let f and g be functions with the following limits. 1. Scalar Multiple: L x f c x = ) ( lim K x g c x = ) ( lim . 1 [ ] bL x f b c x = ) ( lim

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2. Sum or Difference: 3. Product: 4. Quotient: [ ] K L x g x f c x ± = ± ) ( ) ( lim [ ] LK x g x f c x = ) ( ) ( lim 0 , ) ( ) ( lim = K K L x g x f c x
5. Power: [ ] n n c x L x f = ) ( lim

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Thm. 1.3 Limits of Polynomial and Rational Functions If p is a polynomial function and c is a real number, then If r is a rational function given by r(x) = p(x)/q(x) and q(c) 0 Ex. 3 ) ( ) ( lim c p x p c x = ) ( ) ( ) ( ) ( lim c q c p c r x r c x = =
Thm. 1.4 The Limit of a Function Involving a Radical Let n be a positvie integer. The following limit is valid for al c if n is odd, and is valid for c > 0 if n is even.

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