Explanation

If f(x) ≤ g(x) ≤ h(x) near c and:

lim (x→c) f(x) = lim (x→c) h(x) = L

Then lim (x→c) g(x) = L

Example:
−x² ≤ x²sin(1/x) ≤ x² → lim (x→0) x²sin(1/x) = 0

Quiz

1. What is squeezed in the squeeze theorem?

2. If bounds have the same limit, what about middle function?

3. Example bounds? −x² ≤ g(x) ≤ x²

4. lim (x→0) x²sin(1/x) = ?

5. Can it solve tricky oscillating functions?

Answer Key

1. Function between two others

2. It has the same limit

3. −x² and x²

4. 0

5. Yes