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Stewart - Calculus 9/e (Metric) (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 23 / 39

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1/1 0/1 1/1 3/3 2/2 5/5 5/5 6/9 0/3 –/1 0/3 –/1 –/2 0/1 –/1
Total
23/39 (59.0%)

  • Instructions

    Calculus, 9th edition by James Stewart, Daniel Clegg, and Saleem Watson, published by Cengage Learning, is widely renowned for its mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. The WebAssign enhancement to this textbook engages students with immediate feedback, rich tutorial content, video examples, interactive questions, and a media-rich eBook.

    Questions 1, 2, 4, 6, 9, 13, and 15 have Watch Its.

    Questions 1 and 2 have Master Its

    Question 3 includes Enhanced Feedback designed to help guide students to the correct answer.

    Question 4 is an Expanded Problem, which goes beyond the basic exercise and asks the student to show steps of their work or reasoning.

    Question 5 is an Explore It question, which is an interactive resource focusing on the real world applications of Calculus. Explore Its allow Calculus students to work with animations and video explanations to deepen their understanding of key concepts by helping them visualize the concepts they are learning.

    Questions 6 and 7 are questions that require the student to complete a proof.

    Question 8 is an application question focused on an application from engineering.

    Question 9 is a Just In Time exercise to remediate algebra skills required for the section.

    Question 10 is from the challenging set of Problems Plus to stretch students' problem solving skills.

    Question 11 is an application question focused on an application from biology.

    Question 12 uses differential equation grading to test the validity of the answer. Accepts any correct form of the answer and runs student's responses through a series of tests to ensure the assumptions and requirements of the question are met.

    Question 13 illustrates vector grading.

    Question 14 is from one of the four diagnostic tests covering Basic Algebra, Analytic Geometry, Functions, and Geometry.

    Question 15 is a question from the Quick Prep module on trigonometric identities. These modules can be used early in the course, or whenever the review is needed. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

    We have also turned on the display of the solutions after the first submission so you can view them. Normally, instructors elect to display these solutions only after the due date.

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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.

1. 1/1 points  |  Previous Answers SCalc9M 1.8.047.MI. My Notes
Question Part
Points
Submissions Used
1
1/1
11/50
Total
1/1
 
Let
f(x) = 
 cx2 + 8x    if x < 5
x3 − cxif x ≥ 5
.
Find the value of the constant c such that the function f continuous on (−∞, ∞)?
c = Correct: Your answer is correct. seenKey

17/6


Solution or Explanation
f(x) = 
cx2 + 8x    if x < 5
x3 − cxif x ≥ 5
f is continuous on
(−∞, 5) and (5, ∞).
 Now
lim x → 5− f(x) = lim x → 5− (cx2 + 8x) = 25c + 40 and lim x → 5+ f(x) = lim x → 5+ (x3 − cx) = 125 − 5c.
 So f is continuous ⇔
25c + 40 = 125 − 5c ⇔ 30c = 85 ⇔ c =
17
6
.
 Thus, for f to be continuous on
(−∞, ∞), c =
17
6
.

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2. 0/1 points  |  Previous Answers SCalc9M 4.5.003.MI. My Notes
Question Part
Points
Submissions Used
1
0/1
5/50
Total
0/1
 
Evaluate the indefinite integral by using the indicated substitution. (Use C for the constant of integration.)
x2
x3 + 3
 dx,    u = x3 + 3
C{{+29​(x3 +3)(32​)}}
Incorrect: Your answer is incorrect. webMathematica generated answer key


Solution or Explanation
Let
u = x3 + 3.
 Then
du = 3x2 dx
 and
x2 dx = 
1
3
 du,
 so
x2
x3 + 3
 dx		 = 
u
1
3
 du
 
 = 
1
3
 
u3/2
3/2
 + C
 = 
1
3
 · 
2
3
u3/2 + C
 = 
2
9
(x3 + 3)3/2 + C.
Enhanced Feedback
Please try again. Recall the substitution rule for indefinite integrals: If
u = g(x)
 is a differentiable function whose range is an interval I and f is continuous on I, then
f(g(x))g'(x)dx
 = 
f(u)du.

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3. 1/1 points  |  Previous Answers SCalc9M 1.6.046. My Notes
Question Part
Points
Submissions Used
1
1/1
5/50
Total
1/1
 
Find the limit, if it exists. (If an answer does not exist, enter DNE.)
 lim x→−5 
5 − |x|
5 + x
 
1
Correct: Your answer is correct. webMathematica generated answer key


Solution or Explanation
Since
|x| = −x
 for
x < 0,
 we have
lim x→−5 
5 − |x|
5 + x
 = lim x→−5 
5 − (−x)
5 + x
 = lim x→−5 
5 + x
5 + x
 = lim x→−5 1 = 1.
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4. 3/3 points  |  Previous Answers SCalc9M 1.5.027.EP. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/50 1/50 1/50
Total
3/3
 
Consider the following.
lim x→1+ 
x + 8
x − 1
If x is chosen to be sufficiently close to 1 with x greater than 1, then f(x) Correct: Your answer is correct. seenKey

>

 0 and f(x) can be made Correct: Your answer is correct. seenKey

arbitrarily large positive

 .
Determine the infinite limit.
     Correct: Your answer is correct.


Solution or Explanation
lim x→1+ 
x + 8
x − 1
 = ∞
 since the numerator is positive and the denominator approaches 0 from the positive side as
x → 1+.

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5. 2/2 points  |  Previous Answers SCalc9M 5.2.EI.001. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
4/50 4/50
Total
2/2
 
Review the Explore It, then use it to complete the exercise below.
Click here to access the Explore It in a new window.
(a)
For which of the three regions (given on the Explore & Test page of the Explore It) can the disk method alone be used to find the volume of the solid generated by revolving the region around the x-axis? (Select all that apply.)
Correct: Your answer is correct.

(b)
For which of the three regions (given on the Explore & Test page of the Explore It) can the disk method alone be used to find the volume of the solid generated by revolving the region around the y-axis? (Select all that apply.)
Correct: Your answer is correct.

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6. 5/5 points  |  Previous Answers SCalc9M 1.7.015. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
1/1 1/1 1/1 1/1 1/1
1/50 1/50 1/50 1/50 1/50
Total
5/5
 
Prove the statement using the ε, δ definition of a limit.
 lim x → 3 
3 + 
1
3
x
 = 4 
Given ε > 0, we need δ such that if 0 < |x − 3| < δ, then
3 + 
1
3
x
 − 4
  Correct: Your answer is correct. seenKey

< ε

 .
 But
3 + 
1
3
x
 − 4
 < ε ⇔ 
1
3
x − 1
 < ε ⇔ 
1
3
|x − 3| < ε ⇔ |x − 3| < Correct: Your answer is correct. seenKey

3ε

 .
 So if we choose
δ = Correct: Your answer is correct. seenKey

3ε
then
0 < |x − 3| < δ
 right double arrow implies
3 + 
1
3
x
 − 4
 < ε.
 Thus,
lim x → 3 
3 + 
1
3
x
 = 4
 by the definition of a limit.
Illustrate with a graph.

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7. 5/5 points  |  Previous Answers SCalc9M 7.1.057. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
1/1 1/1 1/1 1/1 1/1
2/50 3/50 2/50 2/50 3/50
Total
5/5
 
Use integration by parts to prove the reduction formula.
(ln(x))n dx = x(ln(x))n − n
(ln(x))n − 1 dx
Let u = (ln(x))n, then dv =
dx√√√√
. Then
du = 
nln(x)n−1x​
dx
 and v =
x
. By Equation 2, which states that
u dv = uv − 
v du,
 the integration by parts gives the following.
(ln(x))n dx		 = 
x√4
(ln(x))n − 
x 
nln(x)n−1x​
 dx
 = x(ln(x))n − n
(ln(x))n − 1 dx

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8. 6/9 points  |  Previous Answers SCalc9M 1.7.012. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9
0/1 0/1 0/1 1/1 1/1 1/1 1/1 1/1 1/1
1/50 1/50 1/50 1/50 2/50 2/50 2/50 2/50 2/50
Total
6/9
 
A crystal growth furnace is used in research to determine how best to manufacture crystals used in electric components. For proper growth of the crystal, the temperature must be controlled accurately by adjusting the input power. Suppose the relationship is given by
T(w) = 0.1w2 + 2.156w + 20
where T is the temperature in degrees Celsius and w is the power input in watts.
(a)
How much power is needed to maintain the temperature at 205°C? (Round your answer to two decimal places.)
Incorrect: Your answer is incorrect. seenKey

33.56

 watts
(b)
If the temperature is allowed to vary from 205°C by up to ±1°C, what range of wattage is allowed for the input power? (Round your answers to two decimal places.)
Incorrect: Your answer is incorrect. seenKey

33.45

 watts < w < Incorrect: Your answer is incorrect. seenKey

33.67

 watts
(c)
In terms of the ε, δ definition of
lim x→a f(x) = L,
 identify x.
     Correct: Your answer is correct.
Identify f(x).
     Correct: Your answer is correct.
Identify a.
     Correct: Your answer is correct.
Identify L.
     Correct: Your answer is correct.
What value of ε is given?
Correct: Your answer is correct. seenKey

1

 °C
What is the corresponding value of δ? (Round your answer to two decimal places.)
Correct: Your answer is correct. seenKey

0.11

 watts


Solution or Explanation
(a)
T = 0.1w2 + 2.156w + 20 and T = 205 ⇒ 0.1w2 + 2.156w + 20 = 205 ⇒
 [by the quadratic formula or from the graph]
w ≈ 33.56 watts (w > 0)
(b)
From the graph,
204 ≤ T ≤ 206 ⇒ 33.45 < w < 33.67
(c)
x is the input power. f(x) is the temperature. a is the target input power given in part (a). L is the target temperature given in part (a). ε is the tolerance in the temperature (1). δ is the tolerance in the power input in watts indicated in part (b) (0.11 watts).
The w T-coordinate plane is given. There is 1 curve and 3 lines on the graph.
  • The curve enters the window in the first quadrant, goes up and right becoming more steep, passes through the approximate point (33.45, 204) crossing the first line, passes through the approximate point (33.56, 205) crossing the second line, passes through the approximate point (33.68, 206) crossing the third line, and exits the window in the first quadrant.
  • The first line enters the window in the first quadrant, goes horizontally right, passes through the approximate point (33.45, 204) crossing the curve, and exits the window in the first quadrant.
  • The second line enters the window in the first quadrant, goes horizontally right, passes through the approximate point (33.56, 205) crossing the curve, and exits the window in the first quadrant.
  • The third line enters the window in the first quadrant, goes horizontally right, passes through the approximate point (33.68, 206) crossing the curve, and exits the window in the first quadrant.
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9. 0/3 points  |  Previous Answers SCalc9M 1.6.JIT.003. My Notes
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Points
Submissions Used
1 2 3
0/1 0/1 0/1
2/50 2/50 1/50
Total
0/3
 
Find
f(a), f(a + h),
 and the difference quotient
f(a + h) − f(a)
h
,
 where h ≠ 0.
f(x) = 5 − 3x + 6x2
f(a)
 =
−5+3a−6a2
Incorrect: Your answer is incorrect. webMathematica generated answer key
f(a + h)
 =
−3(a+h)+6(a+h)2
Incorrect: Your answer is incorrect. webMathematica generated answer key
f(a + h) − f(a)
h
 =
​

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10. –/1 points SCalc9M 2.PP.012. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
If
f(x) = 
x42 + x41 + 2
1 + x
,
 calculate
f (42)(3).
 Express your answer using factorial notation:
n! = 1 · 2 · 3 ·    · (n − 1) · n.
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11. 0/3 points  |  Previous Answers SCalc9M 11.2.072. My Notes
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Points
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1 2 3
0/1 –/1 –/1
1/50 0/50 0/50
Total
0/3
 
A patient is injected with a drug every 12 hours. Immediately before each injection the concentration of the drug has been reduced by 90% and the new dose increases the concentration by 2.1 mg/L.
(a)
What is the concentration after three doses?
Incorrect: Your answer is incorrect. seenKey

2.331

 mg/L
(b)
If Cn is the concentration after the nth dose, find a formula for Cn as a function of n.
Cn =
(c)
What is the limiting value of the concentration?
mg/L
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12. –/1 points SCalc9M 9.3.010. My Notes
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–/1
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–/1
 
Solve the differential equation.
dz
dt
 + 2et + z = 0
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13. –/2 points SCalc9M 12.4.019. My Notes
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Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Find two unit vectors orthogonal to both
3, 5, 1
 and
−1, 1, 0
.
(smaller i-value)
(larger i-value)

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14. 0/1 points  |  Previous Answers SCalc9M DT.1.005b. My Notes
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1
0/1
2/50
Total
0/1
 
Simplify the rational expression.
4x2 − 3x − 1
x2 − 25
 · 
x + 5
4x + 1
(x−1)(x−5)−1
Incorrect: Your answer is incorrect. webMathematica generated answer key
If you have had difficulty with this problem, you may wish to consult the Review of Algebra on the website StewartCalculus.com.
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15. –/1 points SCalc9M QP.20.009. My Notes
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1
–/1
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–/1
 
Write the expression in terms of sine only.
9(sin(2x) − cos(2x))


Read more about Topic 20: Trigonometric Identities

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