Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
10th Edition
ISBN: 9781305657861
Author: Soo T. Tan
Publisher: Cengage Learning
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Chapter 7.1, Problem 26E
To determine
To compute: The indefinite integral
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(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
Evaluate the integral using integration by parts.
Sx² cos
(9x) dx
Let f be defined as follows.
y = f(x) = x² - 5x
(a) Find the average rate of change of y with respect to x in the following intervals.
from x = 4 to x = 5
from x = 4 to x = 4.5
from x = 4 to x = 4.1
(b) Find the (instantaneous) rate of change of y at x = 4.
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Chapter 7 Solutions
Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
Ch. 7.1 - Write the formula for integration by parts.Ch. 7.1 - Prob. 2CQCh. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 4ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 6ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 8E
Ch. 7.1 - Prob. 9ECh. 7.1 - Prob. 10ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 16ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 18ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 20ECh. 7.1 - Prob. 22ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 24ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 26ECh. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - In Exercises 29-34, evaluate each definite...Ch. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Find the area of the region under the graph of...Ch. 7.1 - Prob. 38ECh. 7.1 - VELOCITY of A DRAGSTER The velocity of a dragster...Ch. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - ALCOHOL-RELATED TRAFFIC ACCIDENTS As a result of...Ch. 7.1 - AVERAGE PRICE OF A COMMODITY The price of a...Ch. 7.1 - DISTANCE COVERED BY A CAR The velocity of the...Ch. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - FUTURE VALUE OF AN INCOME STREAM The chef-owner of...Ch. 7.1 - Prob. 50ECh. 7.1 - RATE OF RETURN ON AN INVESTMENT Suppose an...Ch. 7.1 - Prob. 52ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 2ECh. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 4ECh. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 8ECh. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - Prob. 16ECh. 7.2 - Prob. 17ECh. 7.2 - Prob. 18ECh. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 24ECh. 7.2 - 4lnxx(2+3)lnxdxCh. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - AMUSEMENT PARK ATTENDANCE The management of...Ch. 7.2 - Prob. 34ECh. 7.2 - GROWTH OF FRUIT FLIES On the basis of data...Ch. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - PRODUCERS' SURPLUS FOR WOMEN'S BOOTS Refer to...Ch. 7.2 - Prob. 40ECh. 7.2 - PRODUCERS' SURPLUS FOR MULTITASK DF.SK LAMPS Refer...Ch. 7.2 - Prob. 42ECh. 7.2 - FRANCHISES Elaine purchased a 10-year franchise...Ch. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.3 - Prob. 1CQCh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - In Exercises 114, use the Trapezoidal Rule and...Ch. 7.3 - Prob. 8ECh. 7.3 - In Exercises 114, use the Trapezoidal Rule and...Ch. 7.3 - Prob. 10ECh. 7.3 - In Exercises 114, use the Trapezoidal Rule and...Ch. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - In Exercises 1522, use the Trapezoidal Rule and...Ch. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - In Exercises 1522, use the Trapezoidal Rule and...Ch. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - SURFACE AREA OF THE JACQUELINE KENNEDY ONASSIS...Ch. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - CONSUMERS SURPLUS FOR SPORTS WATCHES Refer to...Ch. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.4 - a. Define 0f(x)dx, where f is continuous on [a, )...Ch. 7.4 - Prob. 2CQCh. 7.4 - In Exercises 1-4, find the area of the shaded...Ch. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - In Exercises 1-4, find the area of the shaded...Ch. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - In Exercises 5-14. find the area of the region...Ch. 7.4 - Prob. 8ECh. 7.4 - In Exercises 5-14. find the area of the region...Ch. 7.4 - In Exercises 5-14. find the area of the region...Ch. 7.4 - In Exercises 5-14. find the area of the region...Ch. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Find the area of the region bounded by the x-axis...Ch. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - In Exercises 19-46, evaluate each improper...Ch. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - In Exercises 19-46, evaluate each improper...Ch. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - In Exercises 19-46, evaluate each improper...Ch. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - In Exercises 19-46, evaluate each improper...Ch. 7.4 - Prob. 44ECh. 7.4 - In Exercises 19-46, evaluate each improper...Ch. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7.4 - PERPETUAL NET INCOME STREAMS The present value of...Ch. 7.4 - ESTABLISHING A TRUST FUND Becky Wilkinson wants to...Ch. 7.4 - PERPETUAL NET INCOME STREAM The perpetual stream...Ch. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.5 - Prob. 1CQCh. 7.5 - Prob. 2CQCh. 7.5 - Prob. 3CQCh. 7.5 - Prob. 1ECh. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.5 - Prob. 19ECh. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - Prob. 23ECh. 7.5 - Prob. 24ECh. 7.5 - Prob. 25ECh. 7.5 - Prob. 26ECh. 7.5 - Prob. 27ECh. 7.5 - Prob. 28ECh. 7.5 - Prob. 29ECh. 7.5 - Prob. 30ECh. 7.5 - Prob. 31ECh. 7.5 - Prob. 32ECh. 7.5 - Prob. 33ECh. 7 - Prob. 1CRQCh. 7 - Prob. 2CRQCh. 7 - Prob. 3CRQCh. 7 - Prob. 4CRQCh. 7 - Prob. 5CRQCh. 7 - Prob. 6CRQCh. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - In Exercises 1-6, evaluate the integral. 4....Ch. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 1BMCh. 7 - Prob. 2BMCh. 7 - Prob. 3BMCh. 7 - Prob. 4BMCh. 7 - Prob. 5BMCh. 7 - Prob. 6BM
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