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OpenStax - Calculus 1/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 5 / 11

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
0/1 1/1 0/1 1/1 2/2 –/1 0/1 0/2 1/1
Total
5/11 (45.5%)

  • Instructions

    WebAssign is proud to support the open source teaching community through our partnership with OpenStax. Calculus from OpenStax is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. The online WebAssign question content for this title is enriched with links to the eBook and is offered as a low-cost solution.

    Question 1 features a tutorial that walks students through implicit differentiation and also contains a full, worked-out solution. Special grading allows the derivative to be written in any equivalent form. For example, try rewriting the sec2(x2y) term by using the given expression for tan(x2y).

    Question 2 demonstrates indefinite integral grading that enforces the use of C and proper use of absolute values for logarithms, while still allowing for any mathematically equivalent answer.

    Questions 3 and 8 feature interactive 3D visualizations for a surface of revolution and intersection of quadric surfaces, respectively. Students can view the graphs from any perspective, using rotation and zooming, in order to determine the appropriate integral or equation. Question 3 also includes an animation of the generating curve for the surface, and Question 8 handles grading for a list of equations.

    Question 4 exhibits power series grading that requires proper form to be marked as correct. It does not accept technically equivalent answers that are not power series.

    Question 5 contains standard equation grading that accepts any form of the correct equation. For example, try solving for y. This question also shows interval grading, which enforces proper notation.

    Question 6 shows list grading that accepts the four solution values in any order.

    Question 7 illustrates vector grading with an arbitrary constant and scalar multiples allowed.

    Question 9 utilizes differential equation grading for a second-order equation. Any form of the general solution is accepted, and can be written in terms of any constants the student chooses. 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.

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1. 0/1 points  |  Previous Answers OSCalc1 3.8.300-309a.WA.Tut. My Notes
Question Part
Points
Submissions Used
1
0/1
2/100
Total
0/1
 
Calculate the derivative with respect to x.
tan(x2y) = (2x + 5y)3
dy
dx
 =
xsec2(5y)​
Incorrect: Your answer is incorrect. webMathematica generated answer key
Tutorial

Solution or Explanation
Let
tan(x2y) = (2x + 5y)3.
 Then
sec2(x2y)(x2y' + 2xy) = 3(2x + 5y)2(2 + 5y')
x2y' sec2(x2y) + 2xy sec2(x2y) = 6(2x + 5y)2 + 15y'(2x + 5y)2
y'(x2 sec2(x2y) − 15(2x + 5y)2) = 6(2x + 5y)2 − 2xy sec2(x2y)
y' = 
6(2x + 5y)2 − 2xy sec2(x2y)
x2 sec2(x2y) − 15(2x + 5y)2
.
Observe that in the given equation y is not explicitly defined in terms of x. What type of differentiation is required? Since y is a function of x, the derivative with respect to x of an expression in y will require the Chain Rule. Why is the Product Rule and the Chain Rule needed for finding the derivative of
tan(x2y)?

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2. 1/1 points  |  Previous Answers OSCalc1 5.6.348. My Notes
Question Part
Points
Submissions Used
1
1/1
2/100
Total
1/1
 
Use an appropriate substitution to express the trigonometric integral in terms of a composition with logarithms. (Use C for the constant of integration. Remember to use absolute values where appropriate.)
tan(5x) dx
−15​ln|cos(5x)|+C
Correct: Your answer is correct. webMathematica generated answer key


†

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3. 0/1 points  |  Previous Answers OSCalc1 6.4.207. My Notes
Question Part
Points
Submissions Used
1
0/1
1/100
Total
0/1
 
The base of a lamp is constructed by revolving a quarter circle
y = 
2x − x2
 around the y-axis from
x = 1
 to
x = 2.
 Create an integral for the surface area of this curve and compute it.
Interactive 3D GraphInteractive 3D GraphInteractive 3D Graph HelpHelp
loading
.238


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4. 1/1 points  |  Previous Answers OSCalc1 10.2.065. My Notes
Question Part
Points
Submissions Used
1
1/1
3/100
Total
1/1
 
Use partial fractions to find the power series of the function.
5
(x − 4)(x + 1)
∞
n = 0
((−1)1+n+(−1)41+n​)xn
Correct: Your answer is correct. webMathematica generated answer key


†

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5. 2/2 points  |  Previous Answers OSCalc1 11.1.028. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/100 6/100
Total
2/2
 
Convert the parametric equations of a curve into rectangular form. No sketch is necessary.
x = 
t
,  y = 9t + 8
y=9x2+8
Correct: Your answer is correct. webMathematica generated answer key
State the domain of the rectangular form. (Enter your answer using interval notation.)
x is in
[0.0000000000000000000000000000000000000000000000,∞)
Correct: Your answer is correct. webMathematica generated answer key


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6. –/1 points OSCalc1 11.2.079. My Notes
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Points
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1
–/1
0/100
Total
–/1
 
For
x = sin(2t),  y = 2 sin(t) where 0 ≤ t < 2π,
 find all values of t at which a vertical tangent line exists. (Enter your answers as a comma-separated list.)
t =


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7. 0/1 points  |  Previous Answers OSCalc1 12.3.145. My Notes
Question Part
Points
Submissions Used
1
0/1
4/100
Total
0/1
 
Find all two-dimensional vectors a orthogonal to vector
b = 
3, 7
.
 Express the answer in component form. (Let α represent real numbers such that
α ≠ 0.)
a =
⟨−7a3​,α⟩


†

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8. 0/2 points  |  Previous Answers OSCalc1 12.6.356. My Notes
Question Part
Points
Submissions Used
1 2
0/1 –/1
1/100 0/100
Total
0/2
 
A hyperboloid of one sheet,
25x2 + 25y2 − z2 = 25,
 and an elliptic cone,
−25x2 + 75y2 + z2 = 0,
 are represented in the figure along with their intersection curves. Identify the intersection curves and find their equations. (Hint: Find y from the system consisting of the equations of the surfaces.)
Interactive 3D GraphInteractive 3D GraphInteractive 3D Graph HelpHelp
loading
Two hyperbolas of equation
123
Incorrect: Your answer is incorrect. webMathematica generated answer key are situated in planes
(entered as comma-separated lists of equations).


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9. 1/1 points  |  Previous Answers OSCalc1 17.1.013. My Notes
Question Part
Points
Submissions Used
1
1/1
8/100
Total
1/1
 
Find the general solution to the linear differential equation.
y'' + 8y' + 16y = 0
y(x) =
ca​e−4x+cb​e−4xx
Correct: Your answer is correct. webMathematica generated answer key


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