Question 1

Which of the following best describes the definition of a limit in calculus?

Accepted Answer

The value a function approaches as the input gets close to a given value.

Question 2

Given f(x)=4x+2, what is limxx&rarr;1f(x)?

Accepted Answer

6

Question 3

If f(x) is not defined at x=2, but limxx&rarr;2f(x) exists, which statement is true?

Accepted Answer

The limit exists even if the function is not defined at x=2.

Question 4

Consider the function f(x)=x2-4x-2. What is limxx&rarr;2f(x)?

Accepted Answer

4

Question 5

Which scenario describes a case where a limit does NOT exist?

Accepted Answer

The function has a jump discontinuity at the point.

Question 6

Given the graph of f(x) with a vertical asymptote at x=2, what is limxx&rarr;2f(x) most likely to be?

Accepted Answer

Does not exist (unbounded behavior)

Question 7

If f(x) oscillates infinitely as x approaches 3, what can be said about limxx&rarr;3f(x)?

Accepted Answer

The limit does not exist due to oscillation.

Question 8

For the function f(x)=1x, what is limxx&rarr;0f(x)?

Accepted Answer

The limit does not exist (unbounded behavior)

Question 9

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

Accepted Answer

If the left and right limits are not equal, the two-sided limit does not exist.

Question 10

Given the graph of f(x) with a jump at x=3, what is limxx&rarr;3f(x)?

Accepted Answer

The limit does not exist due to the jump.

Question 11

Suppose f(x) is defined piecewise and has a jump at x=2. What is limxx&rarr;2f(x)?

Accepted Answer

The limit does not exist.

Question 12

If f(x) approaches infinity as x approaches 2, what is limxx&rarr;2f(x)?

Accepted Answer

The limit does not exist (unbounded behavior)

Question 13

Which of the following is a correct way to estimate a limit numerically?

Accepted Answer

Create a table of values approaching the point from both sides.

Question 14

Given f(x)=3x2+5x+1, what is limxx&rarr;1f(x)?

Accepted Answer

9

Question 15

A function f(x) is continuous at x=2 if:

Accepted Answer

The limit exists and equals the function value at x=2.

Question 16

If f(x) has a removable discontinuity at x=4, what does this mean?

Accepted Answer

The limit exists but the function is not defined or is defined differently at x=4.

Question 17

Which of the following is true about the graphical approach to limits?

Accepted Answer

The graph helps estimate the value the function approaches near a point.

Question 18

If f(x) is defined as f(x)=2 for x3 and f(x)=5 for x&ge;3, what is limxx&rarr;3f(x)?

Accepted Answer

Does not exist (jump discontinuity)

Limits in Calculus: Numerical, Graphical, and One-Sided Approaches

Study Guide - Practice Questions