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Sect.1.5 Infinite Limits

Sect.1.5 Infinite Limits. Limits at infinity Infinite limits. is undefined at x = 3. From the graph. Consider the rational function. And Table. Left:. Decreases without bound. Right:. Increases without bound. Now find the Limit graphically. NOTE: the function increases

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Sect.1.5 Infinite Limits

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  1. Sect.1.5 Infinite Limits Limits at infinity Infinite limits

  2. is undefined at x = 3 From the graph Consider the rational function And Table Left: Decreases without bound Right: Increases without bound

  3. Now find the Limit graphically NOTE: the function increases or decreases without bound NOTE: not the same infinite limits do not exist

  4. Limits Limits at infinity Infinite Limits

  5. Identifying Infinite Limits Rational functions with undefined points in the denominator • Numerically: table of values • Graphically: examine end behavior • Analytically – compare behavior of numerator and denominator

  6. Find Is the denominator approaching 0- or 0+ Examining the behavior of the denominator

  7. Find Is the denominator approaching 0- or 0+

  8. Infinite Properties • Let c and L be real numbers and let f and g be functions such that L > 0 L < 0

  9. 3) Find if and denominator

  10. Find

  11. Find

  12. HOMEWORK Page 88 # 37-43, 45, 47, and 48 all analytically

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