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Limits at Infinity

Limits at Infinity. Lesson 4.5. What Happens?. We wish to investigate what happens when functions go …. To infinity and beyond …. Limits with Infinity. What happens to a function in the long run. N 1. Rules for Manipulating Limits. Note rules on page 239 Note special limits.

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Limits at Infinity

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  1. Limits at Infinity Lesson 4.5

  2. What Happens? • We wish to investigate what happens when functions go … To infinity and beyond …

  3. Limits with Infinity • What happens to a function in the long run N1

  4. Rules for Manipulating Limits • Note rules on page 239 • Note special limits r is a positive rational number

  5. go to zero Manipulating, Evaluating • Symbolically • Use Calculatorlimit((x+2)/(3x-5),x,+) • Graph and observe

  6. Rational Functions • Leading terms dominate • m = n => limit = an/bm • m > n => limit = 0 • m < n => asymptote linear diagonal or higher power polynomial

  7. Rational Functions • Vertical asymptotes • where denominator = 0 • Y-intercepts • where x = 0 • X-intercepts • where numerator = 0

  8. Example • Find • horizontal asymptote • vertical asymptote(s) • zeros • y-intercept

  9. Example • Find • horizontal asymptote • vertical asymptote(s) • zeros • y-intercept

  10. Limits Involving Trig Functions • Consider f(x) = sin x • As x gets very large, function oscillates between 1 and -1 • Thus no limit • Consider • Squeeze theorem applies • Limit is 0

  11. Assignment • Lesson 4.5 • Page 245 • Exercises 1 – 57 EOOAlso 99, 102

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