$\lim_{x \to a} f(x)$ does not exist

Question 1

Given the function $f(x) = x^2$, what is $\lim_{x 	o \infty} f(x)$?

Accepted Answer

$\infty$

Question 2

For the function $f(x) = \frac{2}{x}$, what is $\lim_{x 	o \infty} f(x)$?

Accepted Answer

$0$

Question 3

If $\lim_{x 	o a^-} f(x) = 3$ and $\lim_{x 	o a^+} f(x) = 5$, what can you conclude about $\lim_{x 	o a} f(x)$?

Accepted Answer

$\lim_{x 	o a} f(x)$ does not exist

Question 4

Given the graph of $f(x)$ with $f(0) = 1$ and $\lim_{x 	o 0} f(x) = 2$, which statement is true?

Accepted Answer

There is a removable discontinuity at $x=0$

Question 5

Evaluate $\lim_{x 	o 0} \frac{1}{x}$.

Accepted Answer

Does not exist

Question 6

If $\lim_{x 	o a^-} f(x) = L$ and $\lim_{x 	o a^+} f(x) = L$, what must be true for $\lim_{x 	o a} f(x)$ to exist?

Accepted Answer

Both one-sided limits must exist and be equal

Question 7

Given $\lim_{x 	o 2} f(x) = 0$ and $\lim_{x 	o 2} g(x) = -\frac{1}{2}$, what is $\lim_{x 	o 2} [f(x) + g(x)]$?

Accepted Answer

$-\frac{1}{2}$

Question 8

Suppose $\lim_{x 	o \infty} 4x + 1$ is evaluated. What is the result?

Accepted Answer

$\infty$

Question 9

If $\lim_{x 	o 0} x^3 = 0$, what is $\lim_{x 	o 0} x^5$?

Accepted Answer

$0$

Question 10

Given the graph of $f(x)$, if $\lim_{x 	o -1} f(x) = 1$ and $f(-1) = 1$, what does this indicate about the function at $x = -1$?

Accepted Answer

The function is continuous at $x = -1$

Question 11

If $\lim_{x 	o 0} f(x) = \infty$, which of the following is true?

Accepted Answer

The function grows without bound as $x$ approaches $0$

Question 12

Evaluate $\lim_{x 	o 0} 10$.

Accepted Answer

$10$

Question 13

If $\lim_{x 	o a} f(x)$ does not exist, which of the following could be a reason?

Accepted Answer

The left and right limits at $x=a$ are not equal

Question 14

Given $\lim_{x 	o 0} x = 0$, what is $\lim_{x 	o 0} 4x$?

Accepted Answer

$0$

Question 15

If $\lim_{x 	o 0} f(x) = 2$ and $\lim_{x 	o 0} g(x) = 3$, what is $\lim_{x 	o 0} [f(x) + g(x)]$?

Accepted Answer

$5$

Question 16

Suppose $\lim_{x 	o 0} f(x) = \infty$ and $\lim_{x 	o 0} g(x) = -\infty$. What is $\lim_{x 	o 0} [f(x) + g(x)]$?

Accepted Answer

Does not exist

Question 17

If $\lim_{x 	o a} f(x) = L$ and $f(a) 
eq L$, what type of discontinuity is present at $x=a$?

Accepted Answer

Removable discontinuity

Question 18

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

Accepted Answer

$0$

Question 19

If $\lim_{x 	o 0^-} f(x) = -1$ and $\lim_{x 	o 0^+} f(x) = 1$, what is $\lim_{x 	o 0} f(x)$?

Accepted Answer

Does not exist

Question 20

Given $\lim_{x 	o \infty} x = \infty$, what is $\lim_{x 	o \infty} (4x + 1)$?

Accepted Answer

$\infty$

Limits and Their Properties in Business Calculus

Study Guide - Practice Questions