Limits and Continuity

Question 1

Which statement describes the piecewise function when x = –6?

Revolt · Accepted Answer

Since ⁡f(x) = –36 and f(x) = –36, the function is continuous when x = –6.

Question 2

According to the graph, the function is only left-continuous when x = and only right-continuous when x = .

Revolt · Accepted Answer

0

Question 3

For the domain value where the discontinuity occurs, c, f(x) = .

Revolt · Accepted Answer

4

Question 4

For the domain value where the discontinuity occurs, c, f(x) = .

Revolt · Accepted Answer

infinite

Question 5

For which values of x is the function continuous? Check all that apply.

Revolt · Accepted Answer

0; 1; 2

Question 6

For which functions can the extreme value theorem be applied? Check all that apply. over the interval [–2, 0] over the interval [4, 10]f(x) = x2 + 1 over the interval (0, 2)f(x) = (x – 2)3 over the interval (–10, –4] over the interval [–3, 3]

Revolt · Accepted Answer

over the interval [4, 10]; over the interval [–3, 3]

Question 7

According to the graph, the function is only left-continuous when x = and only right-continuous when x = .

Revolt · Accepted Answer

3

Question 8

The function has a removable discontinuity when x = , and f(x) = can be used in the extended function to fill the hole.

Revolt · Accepted Answer

3

Question 9

The point of discontinuity occurs when x = .

Revolt · Accepted Answer

0

Question 10

The function has a removable discontinuity when x = , and f(x) = can be used in the extended function to fill the hole.

Revolt · Accepted Answer

1.5

Limits and Continuity Answers

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