1. Limits and Continuity
Connecting Multiple Representations Of Limits — Quiz
Test your understanding of connecting multiple representations of limits with 5 practice questions.
Practice Questions
Question 1
What is the best limit notation for the statement that as $x$ gets closer to $2$, the value of $f(x)$ gets closer to $5$?
Question 2
A table shows values of $f(x)$ near $x=1$:
$$\begin{array}{c|c} x & f(x)\\ \hline 0.9 & 1.8\\ 0.99 & 1.98\\ 1.01 & 2.02\\ 1.1 & 2.2 \end{array}$$
What is the most reasonable value of $\lim_{x\to 1} f(x)$?
$$\begin{array}{c|c} x & f(x)\\ \hline 0.9 & 1.8\\ 0.99 & 1.98\\ 1.01 & 2.02\\ 1.1 & 2.2 \end{array}$$
What is the most reasonable value of $\lim_{x\to 1} f(x)$?
Question 3
If a graph has a hole at the point $(3,4)$ and the curve approaches that hole from both sides, what is the value of $\lim_{x\to 3} f(x)$?
Question 4
Suppose $\lim_{x\to 6} f(x)=10$ and $\lim_{x\to 6} g(x)=3$. What is $\lim_{x\to 6} \bigl(f(x)+g(x)\bigr)$?
Question 5
Which statement best describes continuity at a point $x=a$?