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

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 7 / 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 0/1 0/1 –/1 –/1 2/2 –/1 –/2 –/2 –/1 –/1 –/7
Total
7/25 (28.0%)

  • Instructions

    The Calculus Late 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
    • Socratic feedback on questions available when the student incorrectly answers the question
    • Interactive, multi-part tutorials for every concept

    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 WebAssignCalcLT2 1.4.011c.Tut. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
9/50 4/50 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 WebAssignCalcLT2 1.TF.009. My Notes
Question Part
Points
Submissions Used
1
1/1
4/50
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 WebAssignCalcLT2 1.5.003d. My Notes
Question Part
Points
Submissions Used
1
1/1
1/50
Total
1/1
 
Prove
lim x→−2 |x − 3| = 5
 by finding the maximum δ in terms of ε such that
0 < |x + 2| < δ
 implies
||x − 3| − 5| < ε.
 Hint: What is the sign of
x − 3
 near
x = −2?

δ =
ε
Correct: Your answer is correct.
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4. 0/1 points  |  Previous Answers WebAssignCalcLT2 2.5.007b. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
Find the equation of the tangent line to the curve
f(x) = 3 sin(x) − 2 sec(x)
 at
x = π.

y =
5
Incorrect: Your answer is incorrect.
Recall that
d
dx
(sec(x)) = sec(x) tan(x).
 What is the derivative of the sine function? Given a function and a point, how can the slope of the tangent line to the function at that point be found? What is a point on the described tangent line?
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5. 0/1 points  |  Previous Answers WebassignCalcLT2 5.1.058a. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
Find the derivative of the function y defined implicitly in terms of x.
y = ex + 9y
dy
dx
 =
19ex+9y​
Incorrect: Your answer is incorrect.
Recall how to find the derivative of a function y defined implicitly in terms of x. Treat expressions in x and expressions in y independently. Differentiate both sides of the equation with respect to x, but since
y = y(x),
 the Chain Rule must be applied when taking derivatives of expressions in y. This creates a factor of
dy
dx
 each time a derivative is taken of an expression in y. After differentiating, algebraically manipulate the resulting equation to solve for
dy
dx
 in terms of x and y. What is the derivative of the left side of the equation with respect to x? How should the Chain Rule be applied to find the derivative of the right side of the equation with respect to x? After differentiating, how can the given equation be used to simplify the individual terms?
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6. –/1 points WebassignCalcLT2 5.2.086a.Tut. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Evaluate the definite integral using the Fundamental Theorem of Calculus.
 
36
(1 − 
x
)2
2x
 dx
4
 

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7. –/1 points WebAssignCalcLT2 8.3.001zb.Tut. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Solve the initial value problem.
y' = (x − 1)(y − 4),  y(2) = 4
y =

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8. 2/2 points  |  Previous Answers WebAssignCalcLT2 9.4.001r. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
2/50 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. –/1 points WebAssignCalcLT2 9.7.002w. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find the radius of convergence (R) for the series.
∞
n!
8nn
 xn
n = 1
R =
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10. –/2 points WebAssignCalcLT2 12.2.016d. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Suppose the vectors
v = 
−1, 6, 7
 and
w = 
−3, b, c
 are parallel. What are the values of b and c?
b = 
c = 
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11. –/2 points WebAssignCalcLT2 12.4.001e. 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 + 5k
 and
b = j.

a × b = 
b × a = 
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12. –/1 points WebAssignCalcLT2 14.4.008f.Tut. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Calculate the partial derivative using implicit differentiation.
∂z
∂x
,    x2y + 2y2z + xz2 = 16
∂z
∂x
 =

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13. –/1 points WebAssignCalcLT2 14.4.002a. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Suppose
u = f(x, y),
 where
x = x(s, t, r)
 and
y = y(s, t, r).
 Choose the correct tree diagram that illustrates the dependencies among the different variables.

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14. –/7 points WebAssignCalcLT2 14.4.007d. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
–/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/7
 
Consider the relation
F(x, y) = y3 − 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).



(b) Find
Fx
 and
Fy.

Fx = 
Fy = 


Decide whether or not they are continuous.
    

(c) Evaluate
Fy(1, 0).



(d) The Implicit Function Theorem hold.

(e) Write y as a function of x.
y =
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