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.
Limits at Infinity
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Presentation Transcript
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 N1
Rules for Manipulating Limits • Note rules on page 239 • Note special limits r is a positive rational number
go to zero Manipulating, Evaluating • Symbolically • Use Calculatorlimit((x+2)/(3x-5),x,+) • Graph and observe
Rational Functions • Leading terms dominate • m = n => limit = an/bm • m > n => limit = 0 • m < n => asymptote linear diagonal or higher power polynomial
Rational Functions • Vertical asymptotes • where denominator = 0 • Y-intercepts • where x = 0 • X-intercepts • where numerator = 0
Example • Find • horizontal asymptote • vertical asymptote(s) • zeros • y-intercept
Example • Find • horizontal asymptote • vertical asymptote(s) • zeros • y-intercept
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
Assignment • Lesson 4.5 • Page 245 • Exercises 1 – 57 EOOAlso 99, 102
