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

2. 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

3. 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.

4. 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.

5. 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.

6. 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

7. Properties of Infinite Limits

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

9. Infinite Limits and Vertical Asymptotes
Find vertical asymptotes and infinite limits