1.5 Infinite Limits Objectives: -Students will determine infinite limits from the left and from the right -Students will find and sketch the vertical asymptotes.

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Presentation transcript:

1.5 Infinite Limits Objectives: -Students will determine infinite limits from the left and from the right -Students will find and sketch the vertical asymptotes of the graph of a function

Vertical Asymptote: If f(x) approaches ∞ or -∞ as x→c from the right or left, then the line x= c is a vertical asymptote.

Asymptote or Hiatus Point? A vertical asymptote occurs at any x-value that makes the denominator =0 but numerator ≠0 An x-value that makes the numerator and denominator =0 is a hiatus point

Ex 1)

Ex 2)

Ex 3)

3.5 Limits at Infinity Objectives: -Students will determine finite limits at infinity -Students will determine the horizontal asymptotes, if any, of the graph of the function -Students will determine infinite limits at infinity

Limits at Infinity: Let n = degree of numerator m= degree of denominator n>m, n=m, n<m,

Ex 4)

Ex 5)

Ex 6)