Question 1

Which of the following best describes the limit limx&#x2192;2f(x) if the left-hand and right-hand limits are not equal?

Accepted Answer

The limit does not exist because the function values from both sides do not approach the same value.

Question 2

Given the function f(x)=x2-4x-2, what is limx&#x2192;2f(x)?

Accepted Answer

4

Question 3

If f(x) is defined as f(x)=1 for x3 and f(x)=4 for x&#x2265;3, what is limx&#x2192;3f(x)?

Accepted Answer

The limit does not exist.

Question 4

Which of the following is true about the limit limx&#x2192;01x?

Accepted Answer

The limit does not exist because the function becomes unbounded as x approaches 0.

Question 5

Suppose f(x) is continuous everywhere except at x=2, where it has a vertical asymptote. What can you conclude about limx&#x2192;2f(x)?

Accepted Answer

The limit does not exist because the function is unbounded at x=2.

Question 6

If f(x) is defined for all x and limx&#x2192;5f(x)=7, which of the following must be true?

Accepted Answer

As x approaches 5, f(x) approaches 7.

Question 7

A function f(x) is defined as f(x)=x2+1. What is limx&#x2192;3f(x)?

Accepted Answer

10

Question 8

Which of the following is an example of a limit that does not exist due to oscillation?

Accepted Answer

limx&#x2192;0sin(1x)

Question 9

Given the graph of f(x) has a jump at x=1, with limx&#x2192;1f(x)=3 from the left and =5 from the right, what is limx&#x2192;1f(x)?

Accepted Answer

The limit does not exist.

Question 10

If f(x) is defined as f(x)=2x+1, what is limx&#x2192;4f(x)?

Accepted Answer

9

Question 11

A function f(x) is not defined at x=2, but limx&#x2192;2f(x)=5. Which of the following is true?

Accepted Answer

The function has a removable discontinuity at x=2.

Question 12

If f(x) is given by f(x)=x2+2x+1, what is limx&#x2192;-1f(x)?

Accepted Answer

1

Question 13

Which of the following statements is true about one-sided limits?

Accepted Answer

A one-sided limit examines the behavior of the function as x approaches c from only one side (left or right).

Question 14

Suppose f(x) is defined as f(x)=3x+2. What is limx&#x2192;1f(x)?

Accepted Answer

5

Question 15

A function f(x) is defined as f(x)=1x. What is limx&#x2192;0+f(x)?

Accepted Answer

&#x221E;

Question 16

If f(x) is defined as f(x)=x3+2, what is limx&#x2192;2f(x)?

Accepted Answer

12

Question 17

Which of the following is NOT a reason for a limit to not exist at a point c?

Accepted Answer

The function is defined at c.

Limits in Calculus: Numerical and Graphical Approaches

Study Guide - Practice Questions