AP Calculus BC / Unit 1: Limits and Continuity
1.4 Estimating Limit Values from Tables
Notes
Make a table with $x$-values closer and closer to $c$ on both sides, and look for the value the outputs approach.
- Use values like $c \pm 0.1$, $c \pm 0.01$, $c \pm 0.001$.
- Tables suggest a limit; algebra or graphs confirm it.
Practice
A table shows $f(1.9)=3.8$, $f(1.99)=3.98$, $f(2.01)=4.02$, $f(2.1)=4.2$. The best estimate of $\displaystyle \lim_{x\to2} f(x)$ is:
The outputs close in on 4 from both sides.
Why use values on both sides of $c$ in a limit table?
A two-sided limit needs both sides to approach the same value.
A table for $g$ near $x=0$ shows outputs 1, 10, 100, 1000 as $x \to 0^+$. This suggests:
The values keep increasing without settling, which suggests an infinite limit.
Ready for more? Take the Unit 1 test.