Infinite Limits Lesson 2.5. Previous Mention of Discontinuity  A function can be discontinuous at a point The function goes to infinity at one or both.

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Presentation transcript:

Infinite Limits Lesson 2.5

Previous Mention of Discontinuity  A function can be discontinuous at a point The function goes to infinity at one or both sides of the point, known as a pole  Example Y=Enter this function into the Y= screen of your calculator Use standard zoom

A Special Discontinuity  Using standard-zoom ♦Y  Note results of tables (♦Y)

Definition of Infinite Limits  Given function f defined for all reals on open interval containing c (except possibly x = c)

Definition of Infinite Limits M

Vertical Asymptotes  When f(x) approaches infinity as x → c Note some calculators draw false asymptote  Vertical asymptotes generated by rational functions when g(x) = 0 c

Properties of Infinite Limits  Given Then  Sum/Difference  Product  Quotient

Try It Out  Find vertical asymptote  Find the limit  Determine the one sided limit

Assignment  Lesson 2.5  Page 108  Exercises 1 – 57 EOO, 65, 67, 69