Aim: Isn’t infinite limit an oxymoron? Do Now: Sketch by hand Activity Center: send graph of slant asymptote – y = 2x + 1

Vertical asymptote: at zeros of denominator x = 2 Do Now Vertical asymptote: at zeros of denominator x = 2 x = 2 Slant asymptote: Divide: Poll: limit does not exist What is the ? limit does not exist

How do we determine the Asymptotes Let f be the rational function given by where p(x) and q(x) have no common factors 1. The graph of f has vertical asymptotes at the zeros of q(x). The graph of f has at most one horizontal asymptote, as follows: a) If degree of p < degree of q, then the x-axis (y = 0) is a horizontal asymptote. b) If degree of p = degree of q, then the line y = an/bm is a horizontal asymptote. c) If degree of p > degree of q, then the graph of f has no horizontal asymptote. 3. If the degree of p = degree of q + 1, then there is a slant asymptote which is the quotient of the rational expression.

Vertical Asymptotes and Trig Find the vertical asymptote of x  π Since cotangent is a periodic function the asymptotes are infinite in number: x = nπ where n is an integer.

Definition of Infinite Limits Let f be a function that is defined at every real number in some open interval containing c (except possibly at c itself). The statement means . . . see book.

Properties of Infinite Limits Let c be real numbers and let f and g be functions such that 1. Sum or Difference 2. Product 3. Quotient

Properties of Infinite Limits

Determining Infinite Limits Determine the limit as x approaches 1 from left and right.

Infinite Limits and Vertical Asymptotes Find vertical asymptotes and infinite limits