Thomas' Calculus: Early Transcendentals, Books a la Carte Edition (14th Edition)
14th Edition
ISBN: 9780134439440
Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher: PEARSON
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Chapter 7.2, Problem 21E
To determine
Find the solution for the differential equation
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Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
Chapter 7 Solutions
Thomas' Calculus: Early Transcendentals, Books a la Carte Edition (14th 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 - Evaluate the integrals in Exercises 1–46.
4.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
5.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
6.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
7.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
8.
Ch. 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 - Evaluate the integrals in Exercises 1–46.
14. ∫...Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
15.
Ch. 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 - Evaluate the integrals in Exercises 1–46.
20.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
21. ∫...Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
22. ∫...Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
23.
Ch. 7.1 - Evaluate the integrals in Exercises 1–46.
24.
Ch. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Evaluate the integrals in Exercises 1–46.
27.
Ch. 7.1 - Prob. 28ECh. 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 - Prob. 33ECh. 7.1 - Prob. 34ECh. 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 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Evaluate the integrals in Exercises 1–46.
41.
Ch. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Evaluate the integrals in Exercises 1-46.
46.
Ch. 7.1 - Solve the initial value problems in Exercises...Ch. 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 - The linearization of ex at x = 0
Derive the linear...Ch. 7.1 - Show that for any number a > 1
as suggested by...Ch. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - Prob. 65ECh. 7.1 - Prob. 66ECh. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.1 - Prob. 69ECh. 7.1 - Prob. 70ECh. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.2 - In Exercises 14, show that each function y =...Ch. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - Prob. 4ECh. 7.2 - Prob. 5ECh. 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 - 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 - 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 - Solve the differential equation in Exercises...Ch. 7.2 - Solve the differential equation in Exercises...Ch. 7.2 - Prob. 22ECh. 7.2 - Human evolution continues The analysis of tooth...Ch. 7.2 - Atmospheric pressure Earth’s atmospheric pressure...Ch. 7.2 - Prob. 25ECh. 7.2 - The inversion of sugar The processing of raw sugar...Ch. 7.2 - Prob. 27ECh. 7.2 - Voltage in a discharging capacitor Suppose that...Ch. 7.2 - Cholera bacteria Suppose that the bacteria in a...Ch. 7.2 - Growth of bacteria A colony of bacteria is grown...Ch. 7.2 - Prob. 31ECh. 7.2 - Drug concentration An antibiotic is administered...Ch. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Polonium-210 The half-life of polonium is 139...Ch. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - A beam of unknown temperature An aluminum beam was...Ch. 7.2 - Surrounding medium of unknown temperature A pan of...Ch. 7.2 - Silver cooling in air The temperature of an ingot...Ch. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.3 - Each of Exercises 1–4 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 - Prove the identities
sinh (x + y) = sinh x cosh y...Ch. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 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. 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 - In Exercises 25–36, find the derivative of y with...Ch. 7.3 - Prob. 32ECh. 7.3 - In Exercises 25–36, find the derivative of y with...Ch. 7.3 - Prob. 34ECh. 7.3 - In Exercises 25–36, find the derivative of y with...Ch. 7.3 - Prob. 36ECh. 7.3 - Verify the integration formulas in Exercises...Ch. 7.3 - Verify the integration formulas in Exercises...Ch. 7.3 - Verify the integration formulas in Exercises...Ch. 7.3 - Verify the integration formulas in Exercises...Ch. 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 - Evaluate the integrals in Exercises 41–60.
46.
Ch. 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 - Evaluate the integrals in Exercises 41–60.
50.
Ch. 7.3 - Evaluate the integrals in Exercises 41–60.
51.
Ch. 7.3 - Evaluate the integrals in Exercises 41-60.
52.
Ch. 7.3 - Evaluate the integrals in Exercises 41–60.
53.
Ch. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Evaluate the integrals in Exercises 41–60.
57.
Ch. 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 - Evaluate the integrals in Exercises 67–74 in terms...Ch. 7.3 - Prob. 68ECh. 7.3 - Prob. 69ECh. 7.3 - Prob. 70ECh. 7.3 - Evaluate the integrals in Exercises 67–74 in terms...Ch. 7.3 - Prob. 72ECh. 7.3 - Prob. 73ECh. 7.3 - Prob. 74ECh. 7.3 - Prob. 75ECh. 7.3 - Prob. 76ECh. 7.3 - Prob. 77ECh. 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. 7.4 - Which of the following functions grow faster than...Ch. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - The function ex outgrows any polynomial Show that...Ch. 7.4 - Prob. 21ECh. 7.4 - The function ln x grows slower than any...Ch. 7.4 - Suppose you have three different algorithms for...Ch. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 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. 12GYRCh. 7 - Prob. 13GYRCh. 7 - Prob. 14GYRCh. 7 - Prob. 15GYRCh. 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. 37PECh. 7 - In Exercises 35–38, solve the initial value...Ch. 7 - Prob. 39PECh. 7 - Prob. 40PECh. 7 - Prob. 41PECh. 7 - Prob. 42PECh. 7 - Prob. 1AAECh. 7 - Prob. 2AAECh. 7 - Prob. 3AAECh. 7 - Prob. 4AAECh. 7 - Prob. 5AAECh. 7 - Prob. 6AAECh. 7 - Prob. 7AAECh. 7 - Prob. 8AAECh. 7 - Prob. 9AAECh. 7 - Prob. 10AAE
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