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 gives values of a function near $x=2$:
$$\begin{array}{c|cccc} x & 1.9 & 1.99 & 2.01 & 2.1 \\ \hline f(x) & 3.8 & 3.98 & 4.02 & 4.2 \end{array}$$
What is the best estimate of $\lim_{x\to 2} f(x)$?
$$\begin{array}{c|cccc} x & 1.9 & 1.99 & 2.01 & 2.1 \\ \hline f(x) & 3.8 & 3.98 & 4.02 & 4.2 \end{array}$$
What is the best estimate of $\lim_{x\to 2} f(x)$?
Question 2
A table shows values of $g(x)$ near $x=0$:
$$\begin{array}{c|cccc} x & -0.1 & -0.01 & 0.01 & 0.1 \\ \hline g(x) & 1.9 & 1.99 & 2.01 & 2.1 \end{array}$$
What limit is suggested by the table?
$$\begin{array}{c|cccc} x & -0.1 & -0.01 & 0.01 & 0.1 \\ \hline g(x) & 1.9 & 1.99 & 2.01 & 2.1 \end{array}$$
What limit is suggested by the table?
Question 3
A table gives values of $h(x)$ near $x=5$:
$$\begin{array}{c|cccc} x & 4.9 & 4.99 & 5.01 & 5.1 \\ \hline h(x) & 7 & 7 & 7 & 7 \end{array}$$
What is $\lim_{x\to 5} h(x)$?
$$\begin{array}{c|cccc} x & 4.9 & 4.99 & 5.01 & 5.1 \\ \hline h(x) & 7 & 7 & 7 & 7 \end{array}$$
What is $\lim_{x\to 5} h(x)$?
Question 4
A table shows values of $p(x)$ near $x=3$:
$$\begin{array}{c|cccc} x & 2.9 & 2.99 & 3.01 & 3.1 \\ \hline p(x) & 6.1 & 6.01 & 5.99 & 5.9 \end{array}$$
Which statement is best supported by the table?
$$\begin{array}{c|cccc} x & 2.9 & 2.99 & 3.01 & 3.1 \\ \hline p(x) & 6.1 & 6.01 & 5.99 & 5.9 \end{array}$$
Which statement is best supported by the table?
Question 5
A table gives values of $q(x)$ near $x=1$:
$$\begin{array}{c|cccc} x & 0.9 & 0.99 & 1.01 & 1.1 \\ \hline q(x) & 2.1 & 2.01 & 1.99 & 1.9 \end{array}$$
What is the most reasonable estimate for $\lim_{x\to 1} q(x)$?
$$\begin{array}{c|cccc} x & 0.9 & 0.99 & 1.01 & 1.1 \\ \hline q(x) & 2.1 & 2.01 & 1.99 & 1.9 \end{array}$$
What is the most reasonable estimate for $\lim_{x\to 1} q(x)$?