1. Limits and Continuity
Estimating Limit Values From Tables — Quiz
Test your understanding of estimating limit values from tables with 5 practice questions.
Practice Questions
Question 1
A table shows values of $f(x)$ near $x=2$:
$$\begin{array}{c|ccccc} x & 1.9 & 1.99 & 2.00 & 2.01 & 2.1 \\hline f(x) & 3.8 & 3.98 & 4.00 & 4.02 & 4.2 \end{array}$$
What is the best estimate for $\lim_{x\to 2} f(x)$?
$$\begin{array}{c|ccccc} x & 1.9 & 1.99 & 2.00 & 2.01 & 2.1 \\hline f(x) & 3.8 & 3.98 & 4.00 & 4.02 & 4.2 \end{array}$$
What is the best estimate for $\lim_{x\to 2} f(x)$?
Question 2
A table gives these values for $g(x)$ near $x=0$:
$$\begin{array}{c|cccccc} x & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\hline g(x) & 2.9 & 2.99 & 2.999 & 3.001 & 3.01 & 3.1 \end{array}$$
What value is most reasonable for $\lim_{x\to 0} g(x)$?
$$\begin{array}{c|cccccc} x & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\hline g(x) & 2.9 & 2.99 & 2.999 & 3.001 & 3.01 & 3.1 \end{array}$$
What value is most reasonable for $\lim_{x\to 0} g(x)$?
Question 3
A table for $h(x)$ near $x=5$ is shown below:
$$\begin{array}{c|ccccc} x & 4.9 & 4.99 & 5.00 & 5.01 & 5.1 \\hline h(x) & 12 & 12 & \text{undefined} & 12 & 12 \end{array}$$
What is the most reasonable conclusion about $\lim_{x\to 5} h(x)$?
$$\begin{array}{c|ccccc} x & 4.9 & 4.99 & 5.00 & 5.01 & 5.1 \\hline h(x) & 12 & 12 & \text{undefined} & 12 & 12 \end{array}$$
What is the most reasonable conclusion about $\lim_{x\to 5} h(x)$?
Question 4
A table lists values of $p(x)$ near $x=1$:
$$\begin{array}{c|cccc} x & 0.9 & 0.99 & 1.01 & 1.1 \\hline p(x) & 4.1 & 4.01 & 3.99 & 3.9 \end{array}$$
Which statement best describes $p(1)$ if the table says $p(1)=7$?
$$\begin{array}{c|cccc} x & 0.9 & 0.99 & 1.01 & 1.1 \\hline p(x) & 4.1 & 4.01 & 3.99 & 3.9 \end{array}$$
Which statement best describes $p(1)$ if the table says $p(1)=7$?
Question 5
A table for $q(x)$ near $x=3$ is given:
$$\begin{array}{c|cccc} x & 2.9 & 2.99 & 3.01 & 3.1 \\hline q(x) & 8.1 & 8.01 & 8.01 & 8.1 \end{array}$$
What is the best estimate for $\lim_{x\to 3} q(x)$?
$$\begin{array}{c|cccc} x & 2.9 & 2.99 & 3.01 & 3.1 \\hline q(x) & 8.1 & 8.01 & 8.01 & 8.1 \end{array}$$
What is the best estimate for $\lim_{x\to 3} q(x)$?