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Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall

2021

1.8 Continuity (Homework)

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2021/9/12 下午8:33 1.8 Continuity – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Consider the following graph of the function g.

From the given graph of g, state the numbers at which g is discontinuous. (Enter your answers as a

comma-separated list.)

x =

For this assignment, you submit answers by question parts. The number of submissions remaining

for each question part only changes if you submit or change the answer.

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Your last submission is used for your score.

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1. [–/1 Points] SCALC9 1.8.004.DETAILS MY NOTES ASK YOUR TEACHER

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The graph of a function f is given. (Enter your answers as comma-separated lists.)

(a) At what numbers a does not exist?

a =

(b) At what numbers a is f not continuous?

a =

(c) At what numbers a does exist but f is not continuous at a?

a =

ℹ

f(x)lim

x→a

f(x)lim

x→a

2. [–/3 Points] SCALC9 1.8.006.DETAILS MY NOTES ASK YOUR TEACHER

2021/9/12 下午8:33 1.8 Continuity – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Explain why the function is discontinuous at the given number a. (Select all that apply.)

Sketch the graph of the function.

f(x) = a = −5

if x ≠ −5

1 if x = −5

1

x + 5

f(x) and f(x) are finite, but are not equal.lim

x→−5 +

lim

x→−5 −

f(−5) is defined and f(x) is finite, but they are not equal.lim

x→−5

f(x) is not finite.lim

x→−5

f(−5) is undefined.

none of the above

3. [–/2 Points] SCALC9 1.8.020.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

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Explain why the function is discontinuous at the given number a. (Select all that apply.)

none of the above

Sketch the graph of the function.

f(x) = if x ≠ 2

1 if x = 2

x − 2x

x − 4

2

2 a = 2

f(x) does not exist.lim

x→2

f(2) is undefined.

f(2) is defined and f(x) is finite, but they are not equal.lim

x→2

f(x) and f(x) are finite, but are not equal.lim

x→2 +

lim

x→2 −

4. [–/2 Points] SCALC9 1.8.022.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

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Explain why the function is discontinuous at the given number a. (Select all that apply.)

Sketch the graph of the function.

f(x) = a = 4

if x ≠ 4

8 if x = 4

2x − 7x − 4

x − 4

2

f(x) and f(x) exist, but are not equal.lim

x→4 +

lim

x→4 −

f(x) does not exist.lim

x→4

f(4) and f(x) exist, but are not equal.lim

x→4

f(4) is undefined.

none of the above

5. [–/2 Points] SCALC9 1.8.024.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

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Consider the following function.

(a) Explain why f has a removable discontinuity at x = 6. (Select all that apply.)

(b) Redefine f(6) so that f is continuous at x = 6 (and thus the discontinuity is “removed”).

f(6) =

f(x) = x − 14x + 48

x − 6

2

f(6) and f(x) are finite, but are not equal.lim

x→6

f(x) does not exists.lim

x→6

f(x) is finite.lim

x→6

f(6) is undefined.

none of the above

6. [–/2 Points] SCALC9 1.8.026.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

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Find the values of a and b that make f continuous everywhere.

a =

b =

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7. [–/2 Points] SCALC9 1.8.048.DETAILS
MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
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