University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)
3rd Edition
ISBN: 9780321999610
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Chapter 7.3, Problem 42E
To determine
Find the value of the
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Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(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
Chapter 7 Solutions
University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)
Ch. 7.1 - Evaluate the integrals in Exercises 146. 1. 32dxxCh. 7.1 - Evaluate the integrals in Exercises 1–46.
2.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
3.
Ch. 7.1 - Prob. 4ECh. 7.1 - Evaluate the integrals in Exercises 1–46.
5.
Ch. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Evaluate the integrals in Exercises 1–46.
9.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
10.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
11.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
12.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
13.
Ch. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Evaluate the integrals in Exercises 1–46.
17.
Ch. 7.1 - Prob. 18ECh. 7.1 - Evaluate the integrals in Exercises 1–46.
19.
Ch. 7.1 - Prob. 20ECh. 7.1 - Evaluate the integrals in Exercises 1–46.
21. ∫...Ch. 7.1 - Prob. 22ECh. 7.1 - Evaluate the integrals in Exercises 1–46.
23.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
24.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
25.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
26.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
27.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
28.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
29.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
30.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
31.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
32.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
33.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
34.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
35.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
36.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
37.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
38.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
39.
Ch. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Evaluate the integrals in Exercises 1-46.
42.
Ch. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Evaluate the integrals in Exercises 1-46.
45.
Ch. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 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. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.2 - In Exercises 1–4, show that each function y = f(x)...Ch. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - Prob. 4ECh. 7.2 - In Exercises 5–8, show that each function is a...Ch. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Prob. 8ECh. 7.2 - Solve the differential equation in Exercises...Ch. 7.2 - Prob. 10ECh. 7.2 - Solve the differential equation in Exercises...Ch. 7.2 - Prob. 12ECh. 7.2 - Solve the differential equation in Exercises...Ch. 7.2 - Prob. 14ECh. 7.2 - Solve the differential equation in Exercises...Ch. 7.2 - Solve the differential equation in Exercises...Ch. 7.2 - Solve the differential equation in Exercises...Ch. 7.2 - Prob. 18ECh. 7.2 - Solve the differential equation in Exercises...Ch. 7.2 - Prob. 20ECh. 7.2 - Solve the differential equation in Exercises...Ch. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - Working underwater The intensity L(x) of light x...Ch. 7.2 - Voltage in a discharging capacitor Suppose that...Ch. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Oil depletion Suppose the amount of oil pumped...Ch. 7.2 - Continuous price discounting To encourage buyers...Ch. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Cooling soup Suppose that a cup of soup cooled...Ch. 7.2 - Prob. 42ECh. 7.2 - Surrounding medium of unknown temperature A pan of...Ch. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Lascaux Cave paintings Prehistoric cave paintings...Ch. 7.2 - Prob. 50ECh. 7.3 - Each of Exercises 14 gives a value of sinh x or...Ch. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - In Exercises 13–24, find the derivative of y with...Ch. 7.3 - In Exercises 13–24, find the derivative of y with...Ch. 7.3 - In Exercises 13–24, find the derivative of y with...Ch. 7.3 - In Exercises 13–24, find the derivative of y with...Ch. 7.3 - In Exercises 13–24, find the derivative of y with...Ch. 7.3 - Prob. 18ECh. 7.3 - In Exercises 13–24, find the derivative of y with...Ch. 7.3 - In Exercises 13–24, find the derivative of y with...Ch. 7.3 - In Exercises 13–24, find the derivative of y with...Ch. 7.3 - Prob. 22ECh. 7.3 - In Exercises 13–24, find the derivative of y with...Ch. 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 - Prob. 32ECh. 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 - Prob. 40ECh. 7.3 - Evaluate the integrals in Exercises 41–60.
41.
Ch. 7.3 - Evaluate the integrals in Exercises 41–60.
42.
Ch. 7.3 - Evaluate the integrals in Exercises 41–60.
43.
Ch. 7.3 - Evaluate the integrals in Exercises 41–60.
44.
Ch. 7.3 - Evaluate the integrals in Exercises 41–60.
45.
Ch. 7.3 - Prob. 46ECh. 7.3 - Evaluate the integrals in Exercises 41–60.
47.
Ch. 7.3 - Evaluate the integrals in Exercises 41–60.
48.
Ch. 7.3 - Evaluate the integrals in Exercises 41–60.
49.
Ch. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Prob. 62ECh. 7.3 - Prob. 63ECh. 7.3 - Prob. 64ECh. 7.3 - Prob. 65ECh. 7.3 - Prob. 66ECh. 7.3 - Prob. 67ECh. 7.3 - Prob. 68ECh. 7.3 - Prob. 69ECh. 7.3 - Prob. 70ECh. 7.3 - Prob. 71ECh. 7.3 - Prob. 72ECh. 7.3 - Prob. 73ECh. 7.3 - Prob. 74ECh. 7.3 - Prob. 75ECh. 7.3 - Prob. 76ECh. 7.3 - Skydiving If a body of mass m falling from rest...Ch. 7.3 - Prob. 78ECh. 7.3 - Prob. 79ECh. 7.3 - Prob. 80ECh. 7.3 - Prob. 81ECh. 7.3 - Prob. 82ECh. 7.3 - Prob. 83ECh. 7.3 - Prob. 84ECh. 7.3 - Prob. 85ECh. 7.3 - Prob. 86ECh. 7 - Prob. 1GYRCh. 7 - Prob. 2GYRCh. 7 - Prob. 3GYRCh. 7 - Prob. 4GYRCh. 7 - Prob. 5GYRCh. 7 - Prob. 6GYRCh. 7 - Prob. 7GYRCh. 7 - Prob. 8GYRCh. 7 - Prob. 9GYRCh. 7 - Prob. 10GYRCh. 7 - Prob. 11GYRCh. 7 - Prob. 1PECh. 7 - Prob. 2PECh. 7 - Prob. 3PECh. 7 - Prob. 4PECh. 7 - Prob. 5PECh. 7 - Prob. 6PECh. 7 - Prob. 7PECh. 7 - Prob. 8PECh. 7 - Prob. 9PECh. 7 - Prob. 10PECh. 7 - Prob. 11PECh. 7 - Prob. 12PECh. 7 - Prob. 13PECh. 7 - Prob. 14PECh. 7 - Prob. 15PECh. 7 - Prob. 16PECh. 7 - Prob. 17PECh. 7 - Prob. 18PECh. 7 - Prob. 19PECh. 7 - Prob. 20PECh. 7 - Prob. 21PECh. 7 - Prob. 22PECh. 7 - Prob. 23PECh. 7 - Prob. 24PECh. 7 - Prob. 25PECh. 7 - Prob. 26PECh. 7 - Prob. 27PECh. 7 - Prob. 28PECh. 7 - Prob. 29PECh. 7 - Prob. 30PECh. 7 - Prob. 31PECh. 7 - Prob. 32PECh. 7 - Prob. 33PECh. 7 - Prob. 34PECh. 7 - Prob. 35PECh. 7 - Prob. 36PECh. 7 - Prob. 1AAECh. 7 - Prob. 2AAECh. 7 - Prob. 3AAECh. 7 - Prob. 4AAECh. 7 - Prob. 5AAECh. 7 - Prob. 6AAECh. 7 - Prob. 7AAECh. 7 - Prob. 8AAE
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