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Stewart - Calculus: Early Transcendentals 6e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 8 / 40

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

Last Saved : n/a Saving...  ()

Question
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1 2 3 4 5 6 7 8 9 10 11
1/1 6/6 –/2 –/10 –/2 0/2 –/5 1/4 –/6 –/1 0/1
Total
8/40 (20.0%)
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1. 1/1 points  |  Previous Answers SCalcET6 3.9.004.MI. My Notes
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1/1
 
The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 5 cm and the width is 4 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 SCalcET6 4.1.031.MI.SA. My Notes
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1 2 3 4 5 6
1/1 1/1 1/1 1/1 1/1 1/1
1/50 1/50 1/50 1/50 1/50 1/50
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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 + 6x2 63x
Part 1 of 3
For
f(x) = x3 + 6x2 63x, f '(x) = 3x2 + 12 Correct: Your answer is correct. seenKey

12

x 63 Correct: Your answer is correct. seenKey

63

.
Part 2 of 3
To find the critical points, we must solve f '(x) = 0. We have
0 = 3(x2 + 4x 21) = 3(x + 7 Correct: Your answer is correct. seenKey

7

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

3

).
Part 3 of 3
The critical numbers are:
x = -7 Correct: Your answer is correct. seenKey

-7

(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 points SCalcET6 4.1.036. My Notes
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1 2
/1 /1
0/50 0/50
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/2
 
Find the critical numbers of the function.
h(p) = (p - 4)/(p^2 + 5)
p =
(smaller value)
p =
(larger value)
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4. /10 points SCalcET6 4.1.AE.07. My Notes
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/10
 

EXAMPLE 7 Find the critical numbers of the function.

f(x) = x5/7(6 - x)

SOLUTION The Product Rule gives the following.

f '(x) =
(6 - x) + (x5/7)( )
=- x5/7 +
7x2/7
=
-7x +
7x2/7
=
7x2/7

[The same result could be obtained by first writing f(x) = 6x5/7 - x12/7.] Therefore f ' = 0 if

= 0, that is, x = , and f '(x) does not exist when x = . Thus the critical numbers are (larger) and (smaller).

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5. /2 points SCalcET6 4.3.007.MI. My Notes
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1 2
/1 /1
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/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 = (smaller value)
x = (larger value)
Maple Generated Plot

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6. 0/2 points  |  Previous Answers SCalcET6 4.2.024. My Notes
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1 2
0/1 0/1
1/50 1/50
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0/2
 
Suppose that 4f '(x) ≤ 5 for all values of x. Complete the inequality below.
Incorrect: Your answer is incorrect. f(7) - f(4) ≤ Incorrect: Your answer is incorrect.
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7. /5 points SCalcET6 4.4.001. My Notes
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/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))


(b) lim_(x->a) (f(x))/(p(x))


(c) lim_(x->a) (h(x))/(p(x))


(d) lim_(x->a) (p(x))/(f(x))


(e) lim_(x->a) (p(x))/(q(x))
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8. 1/4 points  |  Previous Answers SCalcET6 4.4.072. My Notes
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/1 /1 /1 1/1
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1/4
 
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

What is the meaning of this limit?
    


(b) For fixed t, use l'Hospital's Rule to calculate the following.
lim_(c->0**+) v =

What can you conclude about the velocity of a falling object in a vacuum?
     Correct: Your answer is correct.
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9. /6 points SCalcET6 4.7.030.MI.SA. My Notes
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/1 /1 /1 /1 /1 /1
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/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 20 ft, find the value of x so that the greatest possible amount of light is admitted.
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10. /1 points SCalcET6 4.9.008. My Notes
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/1
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/1
 
Find the most general antiderivative of the function. Use C for any needed constant. (Check your answer by differentiation.)
f (x) = 9x + 10x1.9
F (x) =
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11. 0/1 points  |  Previous Answers SCalcET6 4.TF.002. My Notes
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0/1
 
Determine whether the statement is true or false.
If f has an absolute minimum value at c, then f '(c) = 0.
     Incorrect: Your answer is incorrect.
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