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Stewart - Calculus: Concepts and Contexts 4/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 38 / 40

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
1/1 6/6 2/2 10/10 2/2 2/2 5/5 4/4 4/6 1/1 1/1
Total
38/40 (95.0%)

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    Here are some textbook questions from Calculus: Concepts and Contexts 4/e by James Stewart published by Brooks/Cole Publishing. Click here for a list of all of the questions coded in WebAssign. This demo assignment allows many submissions and allows you to try another version of the same question for practice.

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1. 1/1 points  |  Previous Answers SCalcCC4 4.1.004.MI. My Notes
Question Part
Points
Submissions Used
1
1/1
10/100
Total
1/1
 
The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When the length is 11 cm and the width is 8 cm, how fast is the area of the rectangle increasing?
Correct: Your answer is correct. cm2/s

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2. 6/6 points  |  Previous Answers SCalcCC4 4.2.025.MI.SA. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
1/1 1/1 1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100 1/100 1/100
Total
6/6
 
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise
Find the critical numbers of the function.
f(x) = x3 + 3x2 − 45x
Part 1 of 3
For
f(x) = x3 + 3x2 − 45x, f '(x) = 3x2 + 6 Correct: Your answer is correct. seenKey

6

 x − 45 Correct: Your answer is correct. seenKey

45

 .
Part 2 of 3
To find the critical points, we must solve f '(x) = 0. We have
0 = 3(x2 + 2x − 15) = 3(x + 5 Correct: Your answer is correct. seenKey

5

 )(x − 3 Correct: Your answer is correct. seenKey

3

 ).
Part 3 of 3
The critical numbers are:
x = -5 Correct: Your answer is correct. seenKey

-5

 (smaller value)
x = 3 Correct: Your answer is correct. seenKey

3

 (larger value)
These are the only critical numbers.
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3. 2/2 points  |  Previous Answers SCalcCC4 4.2.030. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/100 1/100
Total
2/2
 
Find the critical numbers of the function.
h(p) = (p - 3)/(p^2 + 8)
p =
3−√17
Correct: Your answer is correct. (smaller value)
p =
3+√17
Correct: Your answer is correct. (larger value)
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4. 10/10 points  |  Previous Answers SCalcCC4 4.2.AE.05. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10
1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1
1/100 1/100 2/100 2/100 2/100 2/100 2/100 1/100 2/100 1/100
Total
10/10
 
Maple Generated Plot
Video Example
Online Textbook

EXAMPLE 7 Find the critical numbers of the function.

f(x) = x5/9(7 - x)

SOLUTION The Product Rule gives the following.

f '(x) =
59​·(x−(49​))
Correct: Your answer is correct. (7 - x) + (x5/9)( Correct: Your answer is correct. )
=- x5/9 +
5(7−x)
Correct: Your answer is correct.
9x4/9
=
-9x +
35−5x
Correct: Your answer is correct.
9x4/9
=
35−14x
Correct: Your answer is correct.
9x4/9

[The same result could be obtained by first writing f(x) = 7x5/9 - x14/9.] Therefore f ' = 0 if

35−14x
Correct: Your answer is correct. = 0, that is, x = Correct: Your answer is correct. , and f '(x) does not exist when x = Correct: Your answer is correct. . Thus the critical numbers are Correct: Your answer is correct. (larger) and Correct: Your answer is correct. (smaller).

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5. 2/2 points  |  Previous Answers SCalcCC4 4.3.005c.MI. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/100 1/100
Total
2/2
 
The graph of the second derivative f '' of a function f is shown. State the x-coordinates of the inflection points of f.
x = Correct: Your answer is correct. (smaller value)
x = Correct: Your answer is correct. (larger value)
Maple Generated Plot

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6. 2/2 points  |  Previous Answers SCalcCC4 4.3.064. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
4/100 4/100
Total
2/2
 
Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.
Correct: Your answer is correct. ≤ f(7) - f(4) ≤ Correct: Your answer is correct.
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7. 5/5 points  |  Previous Answers SCalcCC4 4.5.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
1/1 1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100 2/100
Total
5/5
 
Consider the given limits (a is a constant, f(x) ≥ 0).
lim_(x->a) f(x) = 0 lim_(x->a) g(x) = 0 lim_(x->a) h(x) = 1
lim_(x->a) p(x) = infinity lim_(x->a) q(x) = infinity
Evaluate each limit below. If a limit is indeterminate, enter INDETERMINATE. (If you need to use -∞ or ∞, enter -INFINITY or INFINITY.)
(a) lim_(x->a) (f(x))/(g(x))
Correct: Your answer is correct.

(b) lim_(x->a) (f(x))/(p(x))
Correct: Your answer is correct.

(c) lim_(x->a) (h(x))/(p(x))
Correct: Your answer is correct.

(d) lim_(x->a) (p(x))/(f(x))
Correct: Your answer is correct.

(e) lim_(x->a) (p(x))/(q(x))
Correct: Your answer is correct.
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8. 4/4 points  |  Previous Answers SCalcCC4 4.5.066. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 1/1 1/1 1/1
2/100 2/100 8/100 2/100
Total
4/4
 
If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account, is given by the following where g is the acceleration due to gravity and c is a positive constant describing air resistance.
v=((mg)/c) \(1-e^(-(ct)\/m)\)

(a) Calculate the following.
lim_(t->infinity) v
mgc​
Correct: Your answer is correct.
What is the meaning of this limit?
     Correct: Your answer is correct.


(b) For fixed t, use l'Hospital's Rule to calculate the following.
lim_(c->0**+) v =
gt
Correct: Your answer is correct.
What can you conclude about the velocity of a falling object in a vacuum?
     Correct: Your answer is correct.
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9. 4/6 points  |  Previous Answers SCalcCC4 4.6.023.MI.SA. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 1/1 1/1 1/1 1/1
0/100 0/100 1/100 1/100 1/100 1/100
Total
4/6
 
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 36 ft, find the value of x so that the greatest possible amount of light is admitted.
Part 1 of 4
Let x be the width and y be the height of the window. Thus, the semi-circle has radius x/2. We must maximize the area of the window,
A = xy + 
π
2
x
2
2
 
.
 The perimeter of the window is
36 = 2y + x + π
x
2
,
 and so:
y = (No Response) seenKey

18

 − 
x
2
 − 
πx
(No Response) seenKey

4
Part 2 of 4
We now have
A = x
18 − 
x
2
 − 
πx
4
 + 
π
8
x2 = 18x − 
1
2
x2 − 
π
8
x2.
 Therefore:
A' = 18 Correct: Your answer is correct. seenKey

18

 −
(
$$1+π2​−π4​
Correct: Your answer is correct. 1+pi/4)x
Part 3 of 4
Solving
0 = A' = 18 − 
1 + 
π
4
x
 gives us
x = 
72 Correct: Your answer is correct. seenKey

72
4 + π
.
Part 4 of 4
Since
A'' = −
1 + 
π
4
 < 0,
 then
x = 
72
4 + π
 gives a maximum. Therefore, when
x = 
72
4 + π
 the greatest possible amount of light is admitted. Rounding to two decimal places gives us
x = 10.08 Correct: Your answer is correct. seenKey

10.08
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10. 1/1 points  |  Previous Answers SCalcCC4 4.8.006. My Notes
Question Part
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1
1/1
2/100
Total
1/1
 
Find the most general antiderivative of the function. Use C for any needed constant. (Check your answer by differentiation.)
f (x) = 9x + 10x1.1
F (x) =
92​x2+102.1​x2.1+C
Correct: Your answer is correct.
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11. 1/1 points  |  Previous Answers SCalcCC4 4.TF.002. My Notes
Question Part
Points
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1
1/1
2/100
Total
1/1
 
Determine whether the statement is true or false.
If f has an absolute minimum value at c, then f '(c) = 0.
     Correct: Your answer is correct.
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