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, Problem 17PE
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4.
The revenue (in thousands of dollars) from producing x units of an item is R(x)=8x-0.015 x².
a) Find the average rate of change of revenue when the production is increased from 1000 to 1001 units.
MATH 122
WORKSHEET 3
February 5, 2025
. Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let f(x) = x² - 2x + 1.
(a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly
evaluating the limit:
f'(0) = lim (
f(Ax) - f(0)
Ax
Ax→0
(b) Find the equation of the tangent line 1 to the graph of ƒ at P.
What are the x and y intercepts of 1 ?
(c) Find the equation of the line, n, through P that is perpendicular to the tangent line l.
(Line n is called the normal line to the graph of f at P.)
(d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its
tangent and normal lines at point P, and the x and y intercepts of these lines.
Bonus: Find the coordinates of the second point, Q, (QP), at which the normal
line n intersects the graph of f.
2. A rock is thrown vertically upward with an initial velocity of 20 m/s
from the edge of a bridge that is 25 meters above a river bed. Based
on Newton's Laws of…
3. Use the graph for problem #35, p175 to answer the questions.
The average price (in cents) per gallon of unleaded gasoline in the United States for the years 2010 to 2019 is
shown in this chart. Find the average rate of change per year in the average price per gallon for each time
period. Source: U.S. Energy Information Administration.
a) 2010 to 2013
b) 2012 to 2018
c) 2014 to 2019
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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