Explanation

To estimate limits from a table:

1. Choose x-values closer to the point of interest from left and right.

2. Observe f(x) values.

3. If values approach the same number → that’s the limit.

Example:
x: 1.9, 1.99, 2.01, 2.1
f(x): 3.1, 3.01, 2.99, 2.9 → lim (x → 2) f(x) ≈ 3

Quiz

1. How do you estimate a limit from a table?

2. Should x-values be close to the point of interest?

3. If left-hand and right-hand values differ, limit = ?

4. Can you use tables for non-linear functions?

5. lim (x → 1) with table f(0.9)=1.8, f(0.99)=1.98, f(1.01)=2.02 → ?

Answer Key

1. Observe f(x) as x approaches the point

2. Yes

3. Does not exist

4. Yes

5. 2