Limits and Continuity

Question 1

Using limits, for which value of x is the function continuous? Check all that apply.

Revolt · Accepted Answer

–2; 0; 5

Question 2

Question 2

Revolt · Accepted Answer

3

Question 3

Question 3

Revolt · Accepted Answer

9

Question 4

Complete the sentences to describe any points of discontinuity in the function The function has a removable point of discontinuity when x = . The function has infinite discontinuity when x = . The function has jump discontinuity when x = .

Revolt · Accepted Answer

–3; Selection 1: –3; Selection 2: 3; Selection 3: 9

Question 5

Use a graphing tool to graph the function and complete the sentences based on the graph of the function . The function has a point of discontinuity when x = where, from the left, the function approaches .

Revolt · Accepted Answer

0; Selection 1: 0; Selection 2: negative infinity

Question 6

Which function is continuous at x = 5?

Revolt · Accepted Answer

f(x) = (x − 5)2 + 6

Question 7

Complete the sentences to describe the function . The function is discontinuous at x = . To create the extended function, add f(x)= .

Revolt · Accepted Answer

Selection 1: 0; Selection 2: -16, x = 0

Question 8

Which functions have a removeable discontinuity? Check all that apply.

Revolt · Accepted Answer

Option A; f (x) = StartFraction x + 7 Over x squared minus 49 EndFraction; f (x) = StartFraction x squared minus 36 Over x + 6 EndFraction

Question 9

Which discontinuities can be seen clearly on any graphing tool? Check all that apply.

Revolt · Accepted Answer

jump; infinite; endpoint

Question 10

Consider the function f(x) = x3 + 34 over the interval [–3, 4]. According to the extreme value theorem, the function has a minimum value of and a maximum value of .

Revolt · Accepted Answer

7; Selection 1: 7; Selection 2: 98

Limits and Continuity Answers

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