RogaCalcET2 2.4.023.Tutorial.SA.

 
Problem Statement

eval rand(5,9);
8-1;

Determine the points of discontinuity. State the type of discontinuity (removable, jump, infinite, or none of these) and whether the function is left- or right-continuous.

 
Step 1

Question 1

The given function is a function and it is continuous .

Correct.
Incorrect.

 
Step 2

Question Sequence

Recall that the domain of a rational function is defined for all values of x except those values for which .

Question 2

Solve for x.

x = .

Correct.
Incorrect.

Question 3

Therefore the domain of is all real numbers except

x =.

Correct.
Incorrect.

Question 4

Because it is a rational function, is continuous over it's domain. Thus, is discontinuous at the point x = since this is the value at which f(x) is not defined.

Correct.
Incorrect.

 
Step 3

Recall the possible types of discontinuities.

Question Sequence

Question 5

If exists but is not equal to , then x = c is a(n) discontinuity.

Correct.
Incorrect.

Question 6

If and exist but are not equal, then x = c is a(n) discontinuity.

Correct.
Incorrect.

Question 7

If one or both of and is infinite, then x = c is a(n) discontinuity even if itself is not defined at x = c.

Correct.
Incorrect.

Question 8

To determine the type of discontinuity at , find the one-sided limits as x approaches .

=

=

(Use "inf" for ∞ and "-inf" for -∞)

Correct.
Incorrect.

Question 9

State the type of discontinuity at .

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 4

Recall the definition of a one-sided continuity at x = c for a given function .

Question 10

If , the function is -continuous at x = c.

If , the function is -continuous at x = c.

Correct.
Incorrect.

Question 11

A graph of the function is shown below (c = 7/8).

At the point of the discontinuity, , the given function is which of the following?

A.
B.
C.
Correct.
Incorrect.
true