Yes, because $\lim_{x \to 3} f(x) = f(3)$

No, because $\lim_{x \to 2} g(x) \neq g(2)$

$\lim_{x \to a} \frac{f(x)}{g(x)} = \frac{\lim_{x \to a} f(x)}{\lim_{x \to a} g(x)}$ if $\lim_{x \to a} g(x) \neq 0$

Question 1

Let $f(x) = 2x + 2$. What is $\lim_{x 	o 2.5} f(x)$?

Accepted Answer

$7$

Question 2

Given $f(x) = x^2 - 9$, what is $\lim_{x 	o 3} f(x)$?

Accepted Answer

$0$

Question 3

Which of the following statements is TRUE about the limit $\lim_{x 	o a} f(x) = L$?

Accepted Answer

For all values of $x$ sufficiently close to $a$, $f(x)$ is close to $L$.

Question 4

Suppose $f(x)$ is defined as $f(x) = \frac{x^2 - 9}{x - 3}$. What is $\lim_{x 	o 3} f(x)$?

Accepted Answer

$6$

Question 5

If $\lim_{x 	o a^-} f(x) = L$ and $\lim_{x 	o a^+} f(x) = L$, what can be concluded?

Accepted Answer

$\lim_{x 	o a} f(x) = L$

Question 6

Evaluate $\lim_{x 	o 0} \sqrt{x^3 + 12}$.

Accepted Answer

$\sqrt{12}$

Question 7

Find $\lim_{x 	o \infty} \frac{4x^3 - 5x^2 + 4x}{2x^3 + 9x^2 + 7}$.

Accepted Answer

$2$

Question 8

Which of the following is NOT a requirement for a function $f(x)$ to be continuous at $x=a$?

Accepted Answer

$f(x)$ is differentiable at $x=a$

Question 9

Given $h(x) = \begin{cases} x^2 - 9 & x < 3 \ 7 & x \geq 3 \end{cases}$, what is $\lim_{x 	o 3^-} h(x)$?

Accepted Answer

$0$

Question 10

Given $h(x) = \begin{cases} x^2 - 9 & x < 3 \ 7 & x \geq 3 \end{cases}$, what is $\lim_{x 	o 3^+} h(x)$?

Accepted Answer

$7$

Question 11

Evaluate $\lim_{x 	o 2} \frac{x^2 + 5x + 1}{x + 2}$.

Accepted Answer

$3.6$

Question 12

If $f(x) = x^2 - 9$, is $f(x)$ continuous at $x=3$?

Accepted Answer

Yes, because $\lim_{x 	o 3} f(x) = f(3)$

Question 13

Evaluate $\lim_{x 	o 3} \frac{x^2 - 7x + 2}{x - 3}$.

Accepted Answer

$-5$

Question 14

Find $\lim_{x 	o \infty} \frac{2x^2 + 5x + 1}{4x^2 + 7}$.

Accepted Answer

$\frac{2}{4}$

Question 15

Suppose $g(x) = \begin{cases} x - 1 & x < 2 \ 1 & x \geq 2 \end{cases}$. Is $g(x)$ continuous at $x=2$?

Accepted Answer

No, because $\lim_{x 	o 2} g(x) 
eq g(2)$

Question 16

Evaluate $\lim_{x 	o 0} \sqrt{x^3 + 12}$ using properties of limits.

Accepted Answer

$\sqrt{12}$

Question 17

If $\lim_{x 	o a} f(x) = 5$ and $\lim_{x 	o a} g(x) = 2$, what is $\lim_{x 	o a} [f(x) + g(x)]$?

Accepted Answer

$7$

Question 18

Which of the following is the correct property for the limit of a quotient?

Accepted Answer

$\lim_{x 	o a} \frac{f(x)}{g(x)} = \frac{\lim_{x 	o a} f(x)}{\lim_{x 	o a} g(x)}$ if $\lim_{x 	o a} g(x) 
eq 0$

Limits and Continuity in Business Calculus

Study Guide - Practice Questions