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Rogawski & Adams - Calculus 3/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 15 / 24

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

Last Saved : n/a Saving...  ()

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Question
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1 2 3 4 5 6 7 8 9 10 11 12 13 14
–/1 –/1 –/1 –/1 –/2 –/3 –/2 –/1 –/3 –/2 –/1 –/4 –/1 –/1
Total
15/24 (62.5%)

  • Instructions

    WebAssign has partnered with W. H. Freeman to deliver an outstanding resource for your calculus course. Our powerful online homework and assessment system, combined with a textbook that presents the main calculus concepts in clear terms, will help you achieve your teaching goals. WebAssign for Rogawski's Calculus, Third Edition will have over 6000 online questions. Every question includes optional detailed solutions, available to students at your discretion. The solutions use the same algorithmic values assigned in the problem, further driving problem-solving mastery. In addition to these solutions, CalcClip tutorial videos, tutorial questions, and a fully searchable eBook linked to questions further enhance student learning.

    Here are some WebAssign questions from Calculus, Third Edition by Jon Rogawski and Colin Adams. In this sample:
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    • Question 1 is a dynamic figure illustrating volumes of revolution. Try moving the slider to rotate the region around the x-axis. Also, try moving the figure to view the solid from different perspectives.
    • Questions 4, 5, and 6 have tutorials.
    • Question 6 features a CalcClip video that walks the student through the problem.
    • Question 8 demonstrates interval grading for the domain, which can grade any canonically equivalent interval and enforce proper notation.
    • Question 10 shows equation grading and accepts any form of the correct tangent line equation.
    • Question 14 is a dynamic figure. Try rotating the surface and zooming in on the center.
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1. –/1 points RogaCalc3 6.4.DF.09.002. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
The region under
y = 9 − x2
 over the interval
[0, 3]
 is revolved about the x-axis. A slider shows this process and displays the resulting solid. A horizontal line segment at a generic value of y between 0 and 9 is also rotated and is a proxy for a (very) thin shell when this solid is decomposed into a collection of such shells.
Which of the following equations does not have a graph that is part of the boundary of the region considered in this figure?
    
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2. –/1 points RogaCalc3 2.1.022. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
The graph represents the position of a moving particle as a function of time t. If the instantaneous velocities of the particle at
t = 1, 2, and 3
 are v1, v2, and v3, respectively, arrange the values of 0, v1, v2, v3, in increasing order.
    
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3. –/1 points RogaCalc3 2.2.011. My Notes
Question Part
Points
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1
–/1
0/50
Total
–/1
 
Evaluate the limit.
lim x→5 (4x + 9)
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4. –/1 points RogaCalc3 2.2.017.Tutorial. My Notes
Question Part
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1
–/1
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–/1
 
Estimate the limit numerically or state that the limit doesn't exist. (Round your answer to four decimal places. If an answer does not exist, enter DNE.)
lim x→25 
x
 − 5
x − 25

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5. –/2 points RogaCalc3 2.4.004.Tutorial. My Notes
Question Part
Points
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1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Consider the graph of a function g(x).
WebAssign Plot
Find the point c at which the function has a jump discontinuity but is right-continuous.
c =

What value should be assigned to g(c) to make g left-continuous at x = c?
g(c) =

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6. –/3 points RogaCalc3 2.4.023.Tutorial. My Notes
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1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Determine the point of discontinuity.
f(x) = 
x + 1
4x − 3
x =

State the type of discontinuity.
    

State whether the function is left- or right-continuous.
    

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7. –/2 points RogaCalc3 2.4.024. My Notes
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1 2
–/1 –/1
0/50 0/50
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–/2
 
Determine the points at which the function is discontinuous. (Enter your answers as a comma-separated list.)
h(z) = 
1 − 4z
z2 − 2z − 8
z =


Classify these as removable, jump, or infinite discontinuities.
    
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8. –/1 points RogaCalc3 2.4.036. My Notes
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1
–/1
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–/1
 
Determine the domain of the function
f(x) = 
3x2 − 3
.
 (Enter your answer using interval notation.)
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9. –/3 points RogaCalc3 2.7.033. My Notes
Question Part
Points
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1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
According to the Michaelis-Menten equation, when an enzyme is combined with a substrate of concentration s (in millimolars), the reaction rate (in micromolars/min) is
R(s) = 
As
K + s
,
where A and K are constants.
(a) Find the limiting reaction rate as the concentration s approaches
∞
 by computing
lim s→∞ R(s).



(b) Find
R(K).

R(K) =


(c) For a certain reaction,
K = 1.25
 mM and
A = 0.3 µM/min.
 For which concentration s is
R(s)
 equal to 75% of its limiting value?
s =
mM.
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10. –/2 points RogaCalc3 3.1.033. My Notes
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1 2
–/1 –/1
0/50 0/50
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–/2
 
Use the limit definition to compute the derivative of the function at
x = 4.
f(x) = x3 + x
f '(4) =


Find an equation of the tangent line at
x = 4.
(Enter your answer as an equation using the variables y and x.)
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11. –/1 points RogaCalc3 3.7.051. My Notes
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1
–/1
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–/1
 
Calculate the following derivative.
d
dx
5
sin(7x)cos(7x)
 =
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12. –/4 points RogaCalc3 3.8.039. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50
Total
–/4
 
Consider the following.
y2 = x3 − 3x + 3
(a) Determine
dy
dx
.

dy
dx
 =


(b) For what values of x is
dy
dx
 = 0?
(Enter your answers as a comma-separated list.)
x =


(c) Determine the coordinates
(x0, y0)
 of the point(s) on the graph of
y2 = x3 − 3x + 3
 at which the tangent line is horizontal.
    


(d) Use your previous answers to decide which of the following is the graph of
y2 = x3 − 3x + 3.

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13. –/1 points RogaCalc3 3.9.016. My Notes
Question Part
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1
–/1
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–/1
 
A road perpendicular to a highway leads to a farmhouse located
a = 1.7
 km away (See figure below).
An automobile travels past the farmhouse at a speed of
v = 55
 km/h. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 3.7 km past the intersection of the highway and the road? (Round your answer to three decimal places.)
km/h
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14. –/1 points RogaCalc3 15.4.DF.06.002. My Notes
Question Part
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1
–/1
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–/1
 
The figure shows a graph of
g(x, y) = 
2xy(x + y)
x2 + y2
 near the origin. This graph can be rotated using the mouse, and it can also be zoomed in. Several magnifications of the graph near the origin are also displayed.
The part of the graph of
z = g(x, y)
 which lies over the line
y = 3x
 in the xy-plane is which of the following?
    
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