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Stewart & Kokoska-Calculus for AP 1/e (Homework)

James Finch

Math - High School, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 14 / 16

Due : Thursday, August 29, 2019 19:00 EDT

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5
–/11 –/1 –/1 –/2 –/1
Total
14/16 (87.5%)

  • Instructions

    Designed to the AP® Calculus curriculum framework, Calculus for AP®: A Complete Course, 1st edition, by James Stewart and Stephen Kokoska, and published by Cengage Learning, combines the experience of recent Chief Reader for the AP® Calculus Reading Stephen Kokoska with James Stewart's mathematical precision and accuracy. AP® Calculus exam preparation questions and exam language prepares students for exam success, while current, real-world data introduces, motivates, and illustrates the concepts of calculus.

    The WebAssign enhancement to this textbook, which includes an interactive eBook, is a fully customizable online solution that empowers students to learn, not just do homework. Insightful tools save time and highlight exactly where students are struggling. Students get an engaging experience, instant feedback, and better outcomes. A total win-win!

    Question 1 is an Active Example (AE) that guide students through the process needed to master a concept.

    Question 2 features an application of the derivative. Included is a Master-It (MI), which provides the student an option to open the same problem with different values in a new window, to be worked through in a step by step manner.

    Question 3 demonstrates how any canonically equivalent expression for the derivative is accepted. Included is a Watch-It video, which provides the student an option to watch a video of the process used to solve a similar problem.

    Question 4 is an Explore It (EI) 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.

    Question 5 uses differential equation grading to test the validity of the answer. To accept any correct form of the answer, the grading runs students' responses through a series of tests to ensure the assumptions and requirements of the question are met. 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.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

Assignment Submission

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.

1. –/11 points SCalcHS1 2.1.AE.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/11
 
WebAssign Plot
Video Example

EXAMPLE 1 Find an equation of the tangent line to the function
y = 4x2
 at the point P(1, 4).

SOLUTION We will be able to find an equation of the tangent line t as soon as we know its slope m. The difficulty is that we know only one point, P, on t, whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point
Q(x, 4x2)
 on the graph (as in the figure) and computing the slope mPQ of the secant line PQ. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.]

We choose
x ≠ 1
 so that
Q ≠ P.
 Then,
mPQ = 
4x2 − 4
x − 1
.
For instance, for the point Q(1.5, 9) we have
mPQ = 
(No Response) seenKey

9

 − 4
(No Response) seenKey

1.5

 − 1
 = 
(No Response) seenKey

5
.5
 = (No Response) seenKey

10

 .
The tables below show the values of mPQ for several values of x close to 1. The closer Q is to P, the closer x is to 1 and, it appears from the tables, the closer mPQ is to (No Response) seenKey

8

 . This suggests that the slope of the tangent line t should be m = (No Response) seenKey

8

 .
x mPQ x mPQ
2 12 0 4
1.5 10 .5 6
1.1 8.4 .9 7.600
1.01 8.040 .99 7.960
1.001 8.004 .999 7.996
We say that the slope of the tangent line is the limit of the slopes of the secant lines, and we express this symbolically by writing
lim Q → P mPQ = m     and    lim x → 1 
4x2 − 4
x − 1
 = (No Response) seenKey

8

 .
Assuming that this is indeed the slope of the tangent line, we use the point-slope form of the equation of a line (see Appendix B) to write the equation of the tangent line through (1, 4) as
y − (No Response) seenKey

4

 = (No Response) seenKey

8

 (x − 1)
    or    
y = (No Response) seenKey

8

 x − (No Response) seenKey

4

 .
The graphs below illustrate the limiting process that occurs in this example. As Q approaches P along the graph, the corresponding secant lines rotate about P and approach the tangent line t.
Your work in question(s) will also be submitted or saved.
Viewing Saved Work Revert to Last Response
2. –/1 points SCalcHS1 3.1.030.MI. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
If a ball is thrown into the air with a velocity of 38 ft/s, its height (in feet) after t seconds is given by y = 38t − 16t2. Find the velocity when t = 1.
(No Response) seenKey

6

 ft/s

Solution or Explanation
Click to View Solution

Need Help? Watch It Master It

Your work in question(s) will also be submitted or saved.
Viewing Saved Work Revert to Last Response
3. –/1 points SCalcHS1 3.3.016. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Differentiate the function.
g(x) = x2(1 − 2x)
g'(x) = (No Response) webMathematica generated answer key


Solution or Explanation
g(x) = x2(1 − 2x) = x2 − 2x3 right double arrow implies g'(x) = 2x − 2(3x2) = 2x − 6x2

Need Help? Watch It

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Viewing Saved Work Revert to Last Response
4. –/2 points SCalcHS1 6.5.EI.001. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
Total
–/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.)


(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.)

Viewing Saved Work Revert to Last Response
5. –/1 points SCalcHS1 8.2.014. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Solve the differential equation.
dz
dt
 + 7et + z = 0
(No Response) webMathematica generated answer key


Solution or Explanation
dz
dt
 + 7et + z = 0   ⇒   
dz
dt
 = −7etez   ⇒  
 
e−z dz		 = −7
et dt   ⇒  
−e−z = −7et + C
e−z = 7et − C
 
1
ez
 = 7et − C
ez = 
1
7et − C
 
z = ln
1
7et − C
 = −ln(7et − C)
Your work in question(s) will also be submitted or saved.
Viewing Saved Work Revert to Last Response
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