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WebAssign - Calculus: Early Transcendentals 2/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 18 / 25

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
3/3 1/1 1/1 1/1 1/1 1/1 –/1 2/2 0/1 –/2 –/2 0/1 1/1 7/7
Total
18/25 (72.0%)

  • Instructions

    The Calculus Early Transcendentals question collection by WebAssign includes more than 5000 peer-reviewed and class-tested questions that have been developed by a team of experienced mathematics educators. The questions cover every concept in both single variable and multivariable calculus and have been designed to support any course design using any textbook, as well as courses using no textbook at all. We invite you to review the sample assignment or try our content to see if it is a good solution for your course. Please contact us if you have any questions!

    Question Collection Features
    • 5000 problems, covering all concepts in single variable and multivariable calculus
    • Comprehensive review of precalculus concepts
    • Detailed worked-out solutions for every question
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    Tutorials, solutions, and feedback are available to students at your discretion and can all be easily adjusted by the assignment settings.

    Click here for a list of all of the questions coded in WebAssign.

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1. 3/3 points  |  Previous Answers WebAssignCalcET2 1.4.011c.Tut. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
2/50 2/50 1/50
Total
3/3
 
Write all horizontal and vertical asymptotes for the function; list any removable discontinuities (holes). (If an answer does not exist, enter DNE.)
f(x) = 
x2 − 2x
x2 − 4
 
vertical asymptote     x =
−2
Correct: Your answer is correct.
horizontal asymptote     y =
1
Correct: Your answer is correct.
hole     x =
2
Correct: Your answer is correct.

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2. 1/1 points  |  Previous Answers WebAssignCalcET2 1.TF.009. My Notes
Question Part
Points
Submissions Used
1
1/1
3/50
Total
1/1
 
Let
f(x)
 be a function, and let a be a real number. If
lim x→a f(x)
 exists, then
f(x)
 is continuous at
x = a.
     Correct: Your answer is correct.
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3. 1/1 points  |  Previous Answers WebAssignCalcET2 1.5.003d. My Notes
Question Part
Points
Submissions Used
1
1/1
3/50
Total
1/1
 
Prove
lim x→−2 |x − 2| = 4
 by finding the maximum δ in terms of ε such that
0 < |x + 2| < δ
 implies
||x − 2| − 4| < ε.
 Hint: What is the sign of
x − 2
 near
x = −2?

δ =
ε
Correct: Your answer is correct.
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4. 1/1 points  |  Previous Answers WebAssignCalcET2 2.5.007b. My Notes
Question Part
Points
Submissions Used
1
1/1
4/50
Total
1/1
 
Find the equation of the tangent line to the curve
f(x) = 6 sin(x) − 5 sec(x)
 at
x = π.

y =
5−6(x−π)
Correct: Your answer is correct.
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5. 1/1 points  |  Previous Answers WebAssignCalcET2 2.7.002h. My Notes
Question Part
Points
Submissions Used
1
1/1
4/50
Total
1/1
 
Find the derivative of the function y defined implicitly in terms of x.
y = ex + 6y
dy
dx
 =
exe6y1−ex6e6y​
Correct: Your answer is correct.
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6. 1/1 points  |  Previous Answers WebAssignCalcET2 4.5.006j.Tut. My Notes
Question Part
Points
Submissions Used
1
1/1
3/50
Total
1/1
 
Evaluate the definite integral using the Fundamental Theorem of Calculus.
 
16
(1 − 
x
)2
2x
 dx
4
 
12​ln(16)−12​ln(4)+2
Correct: Your answer is correct.

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7. –/1 points WebAssignCalcET2 7.3.001zb.Tut. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Solve the initial value problem.
y' = (x − 1)(y − 5),  y(2) = 5
y =

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8. 2/2 points  |  Previous Answers WebAssignCalcET2 8.4.001r. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/50 1/50
Total
2/2
 
Determine whether the series
∞
1
n
 − 1
n = 2
 converges or diverges.
     Correct: Your answer is correct.

Which series do you use for comparison?
1√n​
Correct: Your answer is correct.
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9. 0/1 points  |  Previous Answers WebAssignCalcET2 8.7.002w. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
Find the radius of convergence (R) for the series.
∞
n!
5nn
 xn
n = 1
R =
3
Incorrect: Your answer is incorrect.
Recall that for a power series,
cn(x − a)n,
 the radius of convergence, R, can be found by performing the ratio test on
cn.
 If
lim n → ∞ 
cn + 1
cn
 = α,
 then
R = 
1
a
,
 where
R = 0
 if
α = ∞
 and
R = ∞
 if
α = 0.
 What is the center of the given power series? How can logarithms be used to evaluate
lim n → ∞ 
n
n + 1
n
 
?
 What is the result of the ratio test?
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10. –/2 points WebAssignCalcET2 11.2.016d. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Suppose the vectors
v = 
−1, 6, 2
 and
w = 
−2, b, c
 are parallel. What are the values of b and c?
b = 
c = 
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11. –/2 points WebAssignCalcET2 11.4.001e. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Find a × b and b × a if
a = i + 2k
 and
b = j.

a × b = 
b × a = 
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12. 0/1 points  |  Previous Answers WebAssignCalcET2 13.4.008f.Tut. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
Calculate the partial derivative using implicit differentiation.
∂z
∂x
,    x2y + 4y2z + xz2 = 16
∂z
∂x
 =
n
Incorrect: Your answer is incorrect.
Recall that if z is defined implicitly by
F(x, y, z) = 0,
 then the partial derivative
δz
δx
 is given by 
δz
δx
 = − 
Fx
Fz
,
 provided that
Fz ≠ 0.
 How can the given equation be written so that it is in the form
F(x, y, z) = 0? What is Fx? What is Fz?

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13. 1/1 points  |  Previous Answers WebAssignCalcET2 13.4.002a. My Notes
Question Part
Points
Submissions Used
1
1/1
4/50
Total
1/1
 
Suppose
r = f(x, y),
 where
x = x(s, t, u)
 and
y = y(s, t, u).
 Choose the correct tree diagram that illustrates the dependencies among the different variables.

Correct: Your answer is correct.
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14. 7/7 points  |  Previous Answers WebAssignCalcET2 13.4.007d. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
1/1 1/1 1/1 1/1 1/1 1/1 1/1
1/50 1/50 1/50 1/50 1/50 1/50 1/50
Total
7/7
 
Consider the relation
F(x, y) = y7 − x + 1 = 0.
 Use the following steps to investigate whether
F(x, y) = 0
 defines y as a function of x near the point
(1, 0).
(a) Calculate
F(1, 0).

0
Correct: Your answer is correct.

(b) Find
Fx
 and
Fy.

Fx = 
−1
Correct: Your answer is correct.
Fy = 
7y6
Correct: Your answer is correct.


Decide whether or not they are continuous.
     Correct: Your answer is correct.

(c) Evaluate
Fy(1, 0).

0
Correct: Your answer is correct.

(d) The Implicit Function Theorem Correct: Your answer is correct. hold.

(e) Write y as a function of x.
y =
(x−1)(17​)
Correct: Your answer is correct.
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