Estimate the limits in Exercise numerically. HINT [See Example 1.] Example: Use a...

Estimate the limits in Exercise numerically. HINT [See Example 1.]

Example:

Use a table to estimate the following limits:

Solution

a. We cannot simply substitute x = 2, because the function is not defined at x = 2. (Why?)? Instead, we use a table of values as we did above, with x approaching 2 from both sides.

We notice that as x approaches 2 from either side, f (x) appears to be approaching 12. This suggests that the limit is 12, and we write

b. The function In the following table, we allow x to approach 0 from both sides: