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1.8Continuity-Fal21MATH005A71943SINGLEVARIABLECALCULUSIFall2021_WebAssign.pdf
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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EN
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.
Assignment Scoring
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
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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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 =
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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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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
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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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.)
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
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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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 = 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
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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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 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
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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Find the values of a and b that make f continuous everywhere.
a =
b =
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f(x) = if x < 2
ax − bx + 3 if 2 ≤ x < 3 4x − a + b if x ≥ 3
x − 4 x − 2
2
2
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7. [–/2 Points] SCALC9 1.8.048.DETAILS
MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
