13.1 Finding Limits Numerically and Graphically
Ideas in this lesson
- Estimating limits numerically
- One-sided limits and limits from a graph
Estimating limits numerically · Worked example
For f(x) = 2x, a table near x = 3 gives f(2.99) = 5.98 and f(3.01) = 6.02. Estimate lim_{x→3} f(x).
Answer: 6
The table suggests 6. The stated function also confirms the estimate: since f(x) = 2x is continuous, lim_{x→3} f(x) = 2 · 3 = 6.