1. Continuity and One-Sided limits
Rizzi – Calc BC

2. Continuity – A simple Concept
Baby definition:
No holes or jumps in the graph
Can draw graph without picking up pencil

3. Continuity – Let’s Make it Harder Than it Has to Be
A function f is continuous at point c when these three conditions are met:
f(c) is defined

4. One-Sided Limits

5. Types of Discontinuity
Removable Discontinuity:
Limit on both sides of the discontinuity are the same
Nonremovable Discontinuity:
Limit on both sides of the discontinuity are not the same

6. Example
Find the x-values where f is not continuous. Classify the discontinuities as removable or nonremovable.

7. Intermediate Value THeorem
I’m traveling to Florida. Assuming I take I-75 to get there, can I make it to Florida without passing through Ohio?

8. Intermediate Value Theorem (IVT)
The IVT states that if I have a closed interval where my endpoints are not equal, then I should pass through every output value to get from the left endpoint to the right endpoint.

9. IVT In Fancier Terms
If f is continuous on the closed interval [a, b], f(a) ≠ f(b), and k is any number between f(a) and f(b), then there is at least one number c in [a, b] such that f(c) = k

10. Applying the IVT
Use the IVT to show that f has a zero in the interval [1, 2]

11. AP PREP