MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications
15th Edition
ISBN: 9780137590469
Author: Larry Goldstein / David Lay
Publisher: Pearson Education (US)
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Chapter 9.3, Problem 14E
Evaluate the following definite
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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 9 Solutions
MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications
Ch. 9.1 - (Review) Differentiate the following functions:...Ch. 9.1 - Use the substitution u=3x to determine e3/xx2dx.Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...
Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Figure 1 shows graphs of several functions f(x)...Ch. 9.1 - Figure 2 shows graphs of several functions f(x)...Ch. 9.1 - Determine the following integrals using the...Ch. 9.1 - Determine the following integrals using indicated...Ch. 9.1 - Determine the following integrals using the...Ch. 9.1 - Determine the following integrals using the...Ch. 9.1 - Determine the following integrals by making an...Ch. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Determine the following integrals by making an...Ch. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Determine the following integrals by making an...Ch. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Determine 2x(x2+5)dx by making a substitution....Ch. 9.2 - Evaluate the following integral. xe3xdxCh. 9.2 - Evaluate the following integral. lnxdxCh. 9.2 - Evaluate the following integral. xe5xdxCh. 9.2 - Evaluate the following integral. xex2dxCh. 9.2 - Evaluate the following integral. x(x+7)4dxCh. 9.2 - Evaluate the following integral. x(2x+3)...Ch. 9.2 - Evaluate the following integral. xexdxCh. 9.2 - Evaluate the following integral. x2exdxCh. 9.2 - Evaluate the following integral. xx+1dxCh. 9.2 - Evaluate the following integral. x3+2xdxCh. 9.2 - Evaluate the following integral. e2x(13x)dxCh. 9.2 - Evaluate the following integral. (1+x)2e2xdxCh. 9.2 - Evaluate the following integral. 6xe3xdxCh. 9.2 - Evaluate the following integral. x+2e2xdxCh. 9.2 - Evaluate the following integral. xx+1dxCh. 9.2 - Evaluate the following integral. x2xdxCh. 9.2 - Evaluate the following integral. xlnxdxCh. 9.2 - Evaluate the following integral. x5lnxdxCh. 9.2 - Evaluate the following integral. xcosxdxCh. 9.2 - Evaluate the following integral. xsin8xdxCh. 9.2 - Evaluate the following integral. xln5xdxCh. 9.2 - Evaluate the following integral. x3lnxdxCh. 9.2 - Evaluate the following integral. lnx4dxCh. 9.2 - Evaluate the following integral. ln(lnx)xdxCh. 9.2 - Evaluate the following integral. x2exdxCh. 9.2 - Evaluate the following integral. lnx+1dxCh. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Figure 1 shows graphs of several functions f(x)...Ch. 9.2 - Figure 2 shows graphs of several functions f(x)...Ch. 9.2 - Evaluate xex(x+1)2dx using integration by parts....Ch. 9.2 - Evaluate x7ex4dx. [Hint: First, make a...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Prob. 4ECh. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Prob. 8ECh. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Prob. 13ECh. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals: 1elnxdxCh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - In Exercises 24 and 25, find the area of the...Ch. 9.3 - Prob. 25ECh. 9.4 - Consider 13.4(5x9)2dx. Divide the interval 1x3.4...Ch. 9.4 - Prob. 2CYUCh. 9.4 - Prob. 3CYUCh. 9.4 - Prob. 4CYUCh. 9.4 - Prob. 5CYUCh. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Refer to the graph in Fig. 11. Apply the...Ch. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Approximate the following integrals by the...Ch. 9.4 - Approximate the following integrals by the...Ch. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - The following integrals cannot be evaluated in...Ch. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.4 - Area To determine the amount of water flowing down...Ch. 9.4 - Distance Traveled Upon takeoff, the velocity...Ch. 9.4 - Prob. 28ECh. 9.4 - Prob. 29ECh. 9.4 - Consider 12f(x)dx, where f(x)=3lnx. Make a rough...Ch. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.4 - Technology Exercises In Exercises 3740,...Ch. 9.4 - Prob. 38ECh. 9.4 - Prob. 39ECh. 9.4 - Prob. 40ECh. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.5 - The integral formula is used in many applications...Ch. 9.5 - Prob. 1ECh. 9.5 - Present valueA continuous stream of income is...Ch. 9.5 - Present valueFind the present value of a...Ch. 9.5 - Prob. 4ECh. 9.5 - Present value Find the present value of a...Ch. 9.5 - Present valueA continuous stream of income is...Ch. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.6 - Prob. 1CYUCh. 9.6 - Prob. 2CYUCh. 9.6 - Prob. 3CYUCh. 9.6 - In Exercises 1-12, determine if the given...Ch. 9.6 - Prob. 2ECh. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - In Exercises 1-12, determine if the given...Ch. 9.6 - Prob. 11ECh. 9.6 - Prob. 12ECh. 9.6 - Find the area under the graph of y=1x2forx2.Ch. 9.6 - Prob. 14ECh. 9.6 - Find the area under the graph of y=ex/2forx0.Ch. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - Prob. 18ECh. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 22ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 24ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Prob. 28ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 30ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 32ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 34ECh. 9.6 - Prob. 35ECh. 9.6 - Prob. 36ECh. 9.6 - Prob. 37ECh. 9.6 - Prob. 38ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 40ECh. 9.6 - Prob. 41ECh. 9.6 - Prob. 42ECh. 9.6 - Prob. 43ECh. 9.6 - Prob. 44ECh. 9.6 - Prob. 45ECh. 9.6 - Prob. 46ECh. 9.6 - Prob. 47ECh. 9.6 - Prob. 48ECh. 9.6 - Prob. 49ECh. 9.6 - Prob. 50ECh. 9 - Describe integration by substitution in your own...Ch. 9 - Prob. 2FCCECh. 9 - Prob. 3FCCECh. 9 - Prob. 4FCCECh. 9 - Prob. 5FCCECh. 9 - Prob. 6FCCECh. 9 - Prob. 7FCCECh. 9 - Prob. 8FCCECh. 9 - Prob. 9FCCECh. 9 - Prob. 10FCCECh. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Determine the following indefinite integral:...Ch. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Evaluate the following definite integrals:...Ch. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Evaluate the following improper integrals whenever...Ch. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RE
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