1. Sec 5: Vertical Asymptotes & the Intermediate Value Theorem

2. Definition of a Vertical Asymptote
If f(x) approaches ±∞ as x approaches c from the left or right, then the line x = c is a vertical asymptote.
Vertical Asymptotes can be determined by finding where there is non-removable discontinuity in a rational function.

3. Ex 1: Determine all Vertical Asymptotes
A. C. B. D.

4. INTERMEDIATE VALUE THEOREM
If f is continuous on [a, b] and k is any number between f(a) and f(b), then there is a c in [a, b] such that f(c) = k.

5. Example 1
Use the IVT to show that f(x) = x³ + 2x – 1 has a zero (x-intercept so y = 0) in the interval [0, 1].

6. Example 2
Verify that the IVT applies to the indicated interval and find the value of c that is guaranteed by the theorem.
f(x) = x² - 6x + 8 on the interval [-1, 3] where f(c) = 0.

7. HOMEWORK
Pg 85 #9-15 odds
Pg 78 #83, 84, 95
*check answers in the solution manual

8. Start Unit 2 Test Thursday
Calculating limits with a table (numerically)
Finding limits with a graph
Finding limits analytically: substitution, rationalization, factoring
Properties of Limits
Two Special Trig Limits
Continuity & Discontinuity: Removable & Non-Removable
One-Sided Limits
Existence Theorem
Intermediate Value Theorem
Infinite Limits & their Properties