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Stewart - Calculus 7e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 8 / 68

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

Last Saved : n/a Saving...  ()

Question
Points
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
–/6 0/1 1/1 –/1 1/1 1/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/2 –/2 –/1 0/1 –/2 –/1 –/1 –/1 1/1 1/1 1/1 2/2 –/31 –/3
Total
8/68 (11.8%)
  • Instructions

    This demo is for the new textbook Stewart "Calculus", 7th edition. Not all features in this demo are in a final form; this sample is merely a sneak peek at the up-and-coming features for this textbook.

    Four of these exercises -- #7, #10, #16, and #19 -- use Cengage's new Enhanced Feedback. These exercises deliver additional tips on how to work the problem when a student enters an incorrect response.

    Three of these exercises -- #23, #24, and #25 -- are samples from Section 2.1 of Cengage's new Just-in-Time review, a new resource designed to address the varying levels of student preparedness. At the start of each section, Just-in-Time (JIT) modules consisting of approximately 10 problems are provided to review the prerequisite skills from precalculus used in that section. Instructors can assign the entire module or specific questions from the module. 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.

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. /6 points SCalcET7 2.1.001.MI. My Notes
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Points
Submissions Used
1 2 3 4 5 6
/1 /1 /1 /1 /1 /1
0/50 0/50 0/50 0/50 0/50 0/50
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/6
 
A tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.
t (min)     5 10 15 20 25 30
V (gal)     3475 2185 1225 595 145 0
(a) If P is the point (15, 1225) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with the following values. (Round your answers to one decimal place.)
Q slope
(5, 3475)     
(10, 2185)     
(20, 595)     
(25, 145)     
(30, 0)     


(b) Estimate the slope of the tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal place.)

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2. 0/1 points  |  Previous Answers SCalcET7 1.6.022.MI.NSM. My Notes
Question Part
Points
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1
0/1
1/50
Total
0/1
 
Find a formula for the inverse of the function.
f(x) = 
4x 1
2x + 7
f 1(x) =
2x+74x1
Incorrect: Your answer is incorrect.

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3. 1/1 points  |  Previous Answers SCalcET7 2.5.035.MI.NSM. My Notes
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1
1/1
1/50
Total
1/1
 
Use continuity to evaluate the limit.
lim x1 
8
x
8 + x
3
Correct: Your answer is correct.

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4. /1 points SCalcET7 2.5.045.MI.NSM. My Notes
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1
/1
0/50
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/1
 
For what value of the constant c is the function f continuous on (-, )?
f(x) = 
 cx2 + 6x    if x < 3
x3 cxif x 3
c =

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5. 1/1 points  |  Previous Answers SCalcET7 2.7.007.MI.NSM. My Notes
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1
1/1
2/50
Total
1/1
 
Find an equation of the tangent line to the curve at the point (25, 5).
y
x
y =
.1x+2.5
Correct: Your answer is correct.

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6. 1/1 points  |  Previous Answers SCalcET7 2.7.013.MI.NSM. My Notes
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1
1/1
1/50
Total
1/1
 
If a ball is thrown into the air with a velocity of 59 ft/s, its height (in feet) after t seconds is given by y = 59t - 16t2. Find the velocity when t = 1.
Correct: Your answer is correct. ft/s

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7. /1 points SCalcET7 3.1.023.MI.NSM. My Notes
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1
/1
0/50
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/1
 
Differentiate the following function.
y = (4 x^2 + 8 x + 4)/sqrt(x)
y' =

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8. /1 points SCalcET7 3.2.011.MI.NSM. My Notes
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1
/1
0/50
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/1
 
Differentiate the following function.
F(y) = (1/y^2 - 4/y^4)(y+7 y^3)

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9. /1 points SCalcET7 3.6.019.MI.NSM. My Notes
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1
/1
0/50
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/1
 
Find the derivative of the function. Simplify if possible.
y = arcsin(2x + 5)
y' =

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10. /1 points SCalcET7 3.9.004.MI.NSM. My Notes
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1
/1
0/50
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/1
 
The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 9 cm/s. When the length is 5 cm and the width is 4 cm, how fast is the area of the rectangle increasing?
cm2/s

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11. /1 points SCalcET7 3.9.020.MI.NSM. My Notes
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1
/1
0/50
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/1
 
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 9 m from the dock? (Round your answer to two decimal places.)
m/s

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12. /1 points SCalcET7 3.9.024.MI.NSM. My Notes
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Points
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1
/1
0/50
Total
/1
 
A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 13 ft3/min, how fast is the water level rising when the water is 9 inches deep?
ft/min

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13. /1 points SCalcET7 4.1.033.MI.NSM. My Notes
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1
/1
0/50
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/1
 
Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 900 cm3, the pressure is 100 kPa, and the pressure is increasing at a rate of 10 kPa/min. At what rate is the volume decreasing at this instant?
cm3/min

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14. /2 points SCalcET7 4.1.049.MI.NSM. My Notes
Question Part
Points
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1 2
/1 /1
0/50 0/50
Total
/2
 
Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = 6x3 27x2 72x + 9
[-2, 5]
(min)
(max)

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15. /2 points SCalcET7 4.2.047.MI.NSM. My Notes
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1 2
/1 /1
0/50 0/50
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/2
 
Find the absolute maximum and absolute minimum values of f on the given interval. (Round all answers to one decimal place.)
f(t) = t sqrt(25 - t^2)
[-1, 5]
(min)
(max)

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16. /1 points SCalcET7 4.3.067.MI.NSM. My Notes
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Points
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1
/1
0/50
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/1
 
Find a cubic function, in the form below, that has a local maximum value of 3 at -4 and a local minimum value of 0 at 3.
f (x) = ax3 + bx2 + cx + d
f (x) =

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17. 0/1 points  |  Previous Answers SCalcET7 4.4.057.MI.NSM. My Notes
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1
0/1
2/50
Total
0/1
 
Evaluate the limit.
lim_(x->0) (1 - 6 x)^(1\/x)
Incorrect: Your answer is incorrect.

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18. /2 points SCalcET7 4.7.007.MI.NSM. My Notes
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1 2
/1 /1
0/50 0/50
Total
/2
 
Find the dimensions of a rectangle with perimeter 116 m whose area is as large as possible.
m (smaller value)
m (larger value)

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19. /1 points SCalcET7 4.6.011.MI.NSM. My Notes
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Points
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1
/1
0/50
Total
/1
 
If 1,200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
cm3

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20. /1 points SCalcET7 4.7.046.MI.NSM. My Notes
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1
/1
0/50
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/1
 
A boat leaves a dock at 1:00 P.M. and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 2:00 P.M. How many minutes after 1:00 P.M. were the two boats closest together? (Round your answer to the nearest minute.)
min

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21. /1 points SCalcET7 4.9.069.MI.NSM. My Notes
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1
/1
0/50
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/1
 
A stone was dropped off a cliff and hit the ground with a speed of 88 ft/s. What is the height of the cliff?
ft

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22. 1/1 points  |  Previous Answers SCalcET7 10.3.042.VE. My Notes
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1
1/1
1/50
Total
1/1
 
Watch the video below then answer the adjacent question.
Select the curve with the given polar equation.
r2 = cos(7θ)
Maple Generated Plot
Maple Generated Plot
Maple Generated Plot
Maple Generated Plot

Correct: Your answer is correct.
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23. 1/1 points  |  Previous Answers SCalcET7 2.1.JIT.001.MI. My Notes
Question Part
Points
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1
1/1
1/50
Total
1/1
 
Find the slope of the line through P and Q.
P(0, 0), Q(6, 4)
Correct: Your answer is correct.

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24. 1/1 points  |  Previous Answers SCalcET7 2.1.JIT.002.MI. My Notes
Question Part
Points
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1
1/1
1/50
Total
1/1
 
Find the slope of the line through P and Q.
P(1, 5), Q(5, 8)
Correct: Your answer is correct.

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25. 2/2 points  |  Previous Answers SCalcET7 2.1.JIT.003.MI. My Notes
Question Part
Points
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1 2
1/1 1/1
2/50 2/50
Total
2/2
 
Find the slope-intercept form of the equation of the line passing through the given points.
(1, 1),   (3,  
1
2
)
y =
.75x+1.75
Correct: Your answer is correct.

Sketch the line.
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10

Graph LayersToggle Open/Closed

Submission Data

Correct: Your answer is correct.

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26. /31 points SCalcET7 TEC.Demo.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
/1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
/31
 
  • Concept

    This module allows you to compare the graph of a function along with graphs of its first and second derivatives. You can choose from polynomial, trigonometric, and exponential functions as well as an example of a piecewise-defined function. For each function, you can change the coefficients in the equation and observe the effect on the different graphs. You will notice that some coefficients have a much greater effect on the graphs than others.
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27. /3 points SCalc7 QP.14.N.001. My Notes
Question Part
Points
Submissions Used
1 2 3
/1 /1 /1
0/50 0/50 0/50
Total
/3
 
Topic 14: Root Functions

  • 0. When will I need this in Calculus?

    Functions involving roots appear in examples and applications in calculus. It's important to be able to convert functions that contain root signs to exponent form, to be able to identify the domain of root functions, and to visualize the graphs of some basic root functions.

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