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3.5 Limits at Infinity

3.5 Limits at Infinity. “Official” definition of Horizontal Asymptote. The line y = L is a horizontal asymptote of the graph of f if. is HA. is HA. Rules for finding limits at infinity w/ Rational Functions. If the degree of the numerator is less than the degree of the denominator,

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3.5 Limits at Infinity

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  1. 3.5 Limits at Infinity

  2. “Official” definition of Horizontal Asymptote The line y = L is a horizontal asymptote of the graph of f if is HA is HA

  3. Rules for finding limits at infinity w/ Rational Functions • If the degree of the numerator is less than the degree of the denominator, • then the limit of the rational function is 0. • 2. If the degree of the numerator is the same as the degree of the denominator, • then the limit is the ratio of the leading coefficients. • 3. If the degree of the numerator is greater than the degree of the denominator, • then the limit is DNE (ie. it’s an infinite limit). Do these rules sound familiar to you?

  4. Ex. 1 Find the limit: a) b) c) = 0 (or DNE)

  5. Ex. 2 Find the limit: a) b) When x > 0, so… When x < 0, so…

  6. Ex. 3 Find the limit: =DNE a) So… b) (Squeeze Theorem)

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