1. The Squeeze Theorem and Special Trigonometric Limits
AP Calculus
September 9, 2016
Mrs. Agnew

2. Essential Question Essential Vocabulary
How can we evaluate a limit using the
Squeeze Theorem?
What are the implications of the IVT?
Essential Vocabulary
Squeeze Theorem
Amplitude
Intermediate Value Theorem

3. The Squeeze Theorem
If g(x) is squeezed, or sandwiched, between f(x) and h(x) near a, and if f and h have the same limit L at a, then g is forced to have the same limit L at a.
If f(x) ≤ g(x) ≤ h(x) when x is a, and
, then

4. The Squeeze Theorem Hint to use the Squeeze:
Function behind the limit is really the product of two independent functions.
Usually one of the functions is a trig function, and the other function acts as its amplitude.
Graph the positive and negative amplitude function for visual.
Examples

5. Two Special Trig. Limits
The following “special” trigonometric limits are both direct results of the Squeeze Theorem:
Examples…

6. Homework: 9/9/16
Page 68 # (odd) 74, 75, 76, 89, 93, 95