Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
11th Edition
ISBN: 9781305283831
Author: Tan
Publisher: Cengage Learning
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Textbook Question
Chapter 1.2, Problem 72E
John claims that the following points lie on a line:
Prove or disprove his claim.
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Students have asked these similar questions
(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 1 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
Ch. 1.1 - What can you say about the signs of a and b if the...Ch. 1.1 - Refer to the accompanying figure. a. Given the...Ch. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.1 - Prob. 3ECh. 1.1 - Prob. 4ECh. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - In Exercises 712, refer to the accompanying...Ch. 1.1 - Prob. 8E
Ch. 1.1 - Prob. 9ECh. 1.1 - Prob. 10ECh. 1.1 - Prob. 11ECh. 1.1 - In Exercises 712, refer to the accompanying...Ch. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Prob. 21ECh. 1.1 - In Exercises 2124, find the distance between the...Ch. 1.1 - In Exercises 2124, find the distance between the...Ch. 1.1 - Prob. 24ECh. 1.1 - Find the coordinates of the points that are 10...Ch. 1.1 - Find the coordinates of the points that are 5...Ch. 1.1 - Show that the points (3,4), (3,7), (6,1) and (0,2)...Ch. 1.1 - Show that the triangle with vertices (5,2), (2,5),...Ch. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - TRACKING A CRIMINAL WITH GPS After obtaining a...Ch. 1.1 - PLANNING A GRAND TOUR A grand tour of four cities...Ch. 1.1 - WILL YOU INCUR A DELIVERY CHARGE? A furniture...Ch. 1.1 - OPTIMIZING TRAVEL TIME Towns A, B, C, and D are...Ch. 1.1 - MINIMIZING SHIPPING COSTS FOR A FLEET OF AUTOS...Ch. 1.1 - Prob. 40ECh. 1.1 - PURCHASING AN HDTV ANTENNA Will Barclay wishes to...Ch. 1.1 - DISTANCE BETWEEN TWO CRUISE SHIPS Two cruise ships...Ch. 1.1 - DISTANCE BETWEEN TWO CARGO SHIPS Sailing north at...Ch. 1.1 - WATHING A ROCKET LAUNCH At a distance of 4000 ft...Ch. 1.1 - a. Show that the midpoint of the line segment...Ch. 1.1 - A SCAVENGER HUNT A tree is located 20 yd to the...Ch. 1.1 - Prob. 47ECh. 1.1 - Prob. 48ECh. 1.1 - Let (x1,y1) and (x2,y2) be two points lying in the...Ch. 1.1 - In the Cartesian coordinate system, the two axes...Ch. 1.2 - What is the slope of a nonvertical line? What can...Ch. 1.2 - Give a point-slope form, b the slope-intercept...Ch. 1.2 - Prob. 3CQCh. 1.2 - Prob. 4CQCh. 1.2 - Prob. 1ECh. 1.2 - In Exercises 14, find the slope of the line shown...Ch. 1.2 - Prob. 3ECh. 1.2 - Prob. 4ECh. 1.2 - Prob. 5ECh. 1.2 - For Exercises 510, find the slope of the line that...Ch. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - In Exercise 5-10, find the slope of the line that...Ch. 1.2 - Prob. 11ECh. 1.2 - Given the equation 2x+3y=4, answer the following...Ch. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - In Exercises 19 and 20, determine whether the...Ch. 1.2 - Prob. 20ECh. 1.2 - If the line passing through the points (1,a) and...Ch. 1.2 - If the line passing through the points (a,1) and...Ch. 1.2 - In Exercises 2326, find an equation of the line...Ch. 1.2 - In Exercises 2326, find an equation of the line...Ch. 1.2 - In Exercises 2326, find an equation of the line...Ch. 1.2 - Prob. 26ECh. 1.2 - In Exercises 2730, find an equation of the line...Ch. 1.2 - Prob. 28ECh. 1.2 - In Exercises 2730, find an equation of the line...Ch. 1.2 - Prob. 30ECh. 1.2 - In Exercises 31 and 32, determine whether the...Ch. 1.2 - Prob. 32ECh. 1.2 - In Exercises 3336, find an equation of line that...Ch. 1.2 - Prob. 34ECh. 1.2 - In Exercises 3336, find an equation of line that...Ch. 1.2 - Prob. 36ECh. 1.2 - In Exercise 3742, write the equation in the...Ch. 1.2 - Prob. 38ECh. 1.2 - In Exercise 3742, write the equation in the...Ch. 1.2 - Prob. 40ECh. 1.2 - In Exercise 3742, write the equation in the...Ch. 1.2 - Prob. 42ECh. 1.2 - Find an equation of the horizontal line that...Ch. 1.2 - Find an equation of the vertical line that passes...Ch. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Find an equation of the line that passes through...Ch. 1.2 - Find an equation of the line that passes through...Ch. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - In Exercises 5156, find an equation of the line...Ch. 1.2 - Prob. 54ECh. 1.2 - In Exercises 51-56, find an equation of the line...Ch. 1.2 - Prob. 56ECh. 1.2 - Given that the point P(3,5) lies on the line...Ch. 1.2 - Prob. 58ECh. 1.2 - In Exercises 5964, sketch the straight line...Ch. 1.2 - Prob. 60ECh. 1.2 - In Exercises 5964, sketch the straight line...Ch. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - John claims that the following points lie on a...Ch. 1.2 - Prob. 73ECh. 1.2 - Prob. 74ECh. 1.2 - NUCLEAR PLANT UTILIZATION The United States is not...Ch. 1.2 - Prob. 76ECh. 1.2 - COLLEGE ADMISSIONS Using data compiled by the...Ch. 1.2 - WEIGHT OF WHALES The equation W=3.51L192,...Ch. 1.2 - Prob. 79ECh. 1.2 - DECLINING NUMBER OF PAY PHONES As cell phones...Ch. 1.2 - Prob. 81ECh. 1.2 - IDEAL HEIGHTS AND WEIGHTS FOR WOMEN The Venus...Ch. 1.2 - Prob. 83ECh. 1.2 - CORPORATE FRAUD The number of pending corporate...Ch. 1.2 - Prob. 85ECh. 1.2 - Prob. 86ECh. 1.2 - Is there a difference between the statements "The...Ch. 1.2 - Prob. 88ECh. 1.2 - Prob. 89ECh. 1.2 - Prob. 90ECh. 1.2 - Prob. 91ECh. 1.2 - Prob. 92ECh. 1.2 - Prob. 93ECh. 1.2 - Prob. 94ECh. 1.2 - Prob. 95ECh. 1.2 - Prove that if a line L1 with slope m1 is...Ch. 1.2 - Prob. 1TECh. 1.2 - Prob. 2TECh. 1.2 - Prob. 3TECh. 1.2 - Prob. 4TECh. 1.2 - Prob. 5TECh. 1.2 - Prob. 6TECh. 1.2 - Prob. 7TECh. 1.2 - Prob. 8TECh. 1.2 - Prob. 9TECh. 1.2 - Prob. 10TECh. 1.2 - Prob. 11TECh. 1.2 - Prob. 12TECh. 1.3 - a. What is a function? Give an example. b. What is...Ch. 1.3 - What is the general form of a linear cost...Ch. 1.3 - Is the slope of a linear demand curve positive or...Ch. 1.3 - The value of an investment in dollars after t...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - Prob. 4ECh. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - Prob. 6ECh. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - A manufacturer has a monthly fixed cost of 40,000...Ch. 1.3 - A manufacturer has a monthly fixed cost of 10,000...Ch. 1.3 - Find the constants m and b in the linear function...Ch. 1.3 - Find the constants m and b in the linear function...Ch. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - CONSUMPTION FUNCTIONS A certain economys...Ch. 1.3 - SALES TAX In a certain state, the sales tax T on...Ch. 1.3 - SOCIAL SECURITY COLAs Social Security recipients...Ch. 1.3 - PROFIT FUNCTION FOR DIGITAL TIMERS Auto Time, a...Ch. 1.3 - PROFIT FUNCTION FOR LIGHT BULBS The management of...Ch. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - LINEAR DEPRECIATION Suppose an asset has an...Ch. 1.3 - LINEAR DEPRECIATION OF AN OFFICE BUILDING Rework...Ch. 1.3 - Prob. 26ECh. 1.3 - DRUG DOSAGES FOR CHILDREN A method sometime used...Ch. 1.3 - DRUG DOSAGES FOR CHILDREN Cowlings Rule is a...Ch. 1.3 - DRINKING AND DRIVING AMONG HIGH SCHOOL STUDENTS...Ch. 1.3 - CALIFORNIA EMISSIONS CAPS The California emissions...Ch. 1.3 - Prob. 31ECh. 1.3 - U.S. AIRPLANE PASSENGER PROJECTIONS In a report...Ch. 1.3 - CELSIUS AND FAHRENHEIT TEMPERATURES The...Ch. 1.3 - CRICKET CHIRPING AND TEMPERATURE Entomologists...Ch. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - DEMAND FUNCTION FOR A COMMODITY At a unit price...Ch. 1.3 - Prob. 40ECh. 1.3 - DEMAND FUNCTION FOR A COMMODITY Assume that a...Ch. 1.3 - DEMAND FUNCTION FOR A SPORTS WATCH The demand...Ch. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.3 - SUPPLY FUNCTION FOR A DIGITAL RECORDER Suppliers...Ch. 1.3 - SUPPLY FUNCTION FOR A REFRIGERATOR Producers of a...Ch. 1.3 - DEMAND FOR WIRELESS LOUDSPEAKERS The demand...Ch. 1.3 - DEMAND FORWASHABLE COMPUTER KEYBOARDS The demand...Ch. 1.3 - Prob. 51ECh. 1.3 - Prob. 52ECh. 1.3 - Prob. 53ECh. 1.3 - Prob. 54ECh. 1.3 - Prob. 1TECh. 1.3 - Prob. 2TECh. 1.3 - Prob. 3TECh. 1.3 - Prob. 4TECh. 1.3 - Prob. 5TECh. 1.3 - Prob. 6TECh. 1.3 - Prob. 7TECh. 1.3 - Prob. 8TECh. 1.4 - Explain why you would expect that the intersection...Ch. 1.4 - In the accompanying figure, C(x) is the cost...Ch. 1.4 - The accompanying figure gives the demand curve and...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 1-6, find the point of intersection...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 710, find the break-even point for...Ch. 1.4 - In Exercises 710, find the break-even point for...Ch. 1.4 - In Exercises 710, find the break-even point for...Ch. 1.4 - In Exercises 710, find the break-even point for...Ch. 1.4 - BREAK-EVEN ANALYSIS Auto Time, a manufacturer of...Ch. 1.4 - BREAK-EVEN ANALYSIS A division of Carter...Ch. 1.4 - BREAK-EVEN ANALYSIS A division of the Gibson...Ch. 1.4 - LEASING A TRUCK Ace Truck Leasing Company leases a...Ch. 1.4 - DECISION ANALYSIS A product may be made by using...Ch. 1.4 - ANNUAL SALES OF TWO PHARMACIES The annual sales of...Ch. 1.4 - LCDs VERSUS CRTs The global shipments of...Ch. 1.4 - DIGITAL VERSUS FILM CAMERAS The sales of digital...Ch. 1.4 - U.S. FINANCIAL TRANSACTIONS The percentage of U.S....Ch. 1.4 - BROADBAND VERSUS DIAL-UP The number of U.S....Ch. 1.4 - Prob. 21ECh. 1.4 - For each pair of supply-and-demand equations in...Ch. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - EQUILIBRIUM QUANTITY AND PRICE FOR DVD PLAYERS The...Ch. 1.4 - EQUILIBRIUM QUANTITY AND PRICE FOR GPS NAVIGATORS...Ch. 1.4 - 27. EQUILIBRIUM QUANTITY AND PRICE FOR TABLET...Ch. 1.4 - 28. EQUILIBRIUM QUANTITY AND PRICE FOR ESPRESSO...Ch. 1.4 - EQUILIBRIUM QUANTITY AND PRICE FOR WIRELESS...Ch. 1.4 - Prob. 30ECh. 1.4 - Suppose the demand and supply equations for a...Ch. 1.4 - Suppose the cost function associated with a...Ch. 1.4 - In Exercises 33 and 34, determine whether the...Ch. 1.4 - Prob. 34ECh. 1.4 - Let L1 and L2 be two nonvertical straight lines in...Ch. 1.4 - Prob. 36ECh. 1.4 - Prob. 1TECh. 1.4 - Prob. 2TECh. 1.4 - Prob. 3TECh. 1.4 - Prob. 4TECh. 1.4 - Prob. 5TECh. 1.4 - Prob. 6TECh. 1.4 - Prob. 7TECh. 1.4 - BREAK-EVEN ANALYSIS The Monde Company makes a wine...Ch. 1.4 - Prob. 9TECh. 1.4 - Prob. 10TECh. 1.4 - Prob. 11TECh. 1.4 - Prob. 12TECh. 1.5 - Explain the terms (a) scatter diagram (b)...Ch. 1.5 - Prob. 2CQCh. 1.5 - Prob. 1ECh. 1.5 - Prob. 2ECh. 1.5 - Prob. 3ECh. 1.5 - Prob. 4ECh. 1.5 - Prob. 5ECh. 1.5 - In Exercises 16, a find the equation of the least...Ch. 1.5 - COLLEGE ADMISSIONS The accompanying data were...Ch. 1.5 - Prob. 8ECh. 1.5 - Prob. 9ECh. 1.5 - Prob. 10ECh. 1.5 - Prob. 11ECh. 1.5 - Prob. 12ECh. 1.5 - Prob. 13ECh. 1.5 - Prob. 14ECh. 1.5 - Prob. 15ECh. 1.5 - Prob. 16ECh. 1.5 - Prob. 17ECh. 1.5 - Prob. 18ECh. 1.5 - Prob. 19ECh. 1.5 - Prob. 20ECh. 1.5 - Prob. 21ECh. 1.5 - Prob. 22ECh. 1.5 - BOUNCED-CHECK CHARGES Overdraft fees have become...Ch. 1.5 - Prob. 24ECh. 1.5 - Prob. 25ECh. 1.5 - Prob. 26ECh. 1.5 - Prob. 27ECh. 1.5 - Prob. 28ECh. 1.5 - Prob. 29ECh. 1.5 - Prob. 30ECh. 1.5 - Prob. 1TECh. 1.5 - Prob. 2TECh. 1.5 - Prob. 3TECh. 1.5 - Prob. 4TECh. 1.5 - Prob. 5TECh. 1.5 - Prob. 6TECh. 1.5 - Prob. 7TECh. 1.5 - Prob. 8TECh. 1.5 - Prob. 9TECh. 1.5 - Prob. 10TECh. 1.CRQ - Prob. 1CRQCh. 1.CRQ - Prob. 2CRQCh. 1.CRQ - Prob. 3CRQCh. 1.CRQ - Prob. 4CRQCh. 1.CRQ - Prob. 5CRQCh. 1.CRQ - Prob. 6CRQCh. 1.CRQ - Prob. 7CRQCh. 1.CRQ - Prob. 8CRQCh. 1.CRQ - Prob. 9CRQCh. 1.CRQ - Prob. 10CRQCh. 1.CRQ - Prob. 11CRQCh. 1.CRQ - Prob. 12CRQCh. 1.CRE - Prob. 1CRECh. 1.CRE - Prob. 2CRECh. 1.CRE - Prob. 3CRECh. 1.CRE - Prob. 4CRECh. 1.CRE - Prob. 5CRECh. 1.CRE - Prob. 6CRECh. 1.CRE - Prob. 7CRECh. 1.CRE - Prob. 8CRECh. 1.CRE - Prob. 9CRECh. 1.CRE - Prob. 10CRECh. 1.CRE - Prob. 11CRECh. 1.CRE - Prob. 12CRECh. 1.CRE - Prob. 13CRECh. 1.CRE - Prob. 14CRECh. 1.CRE - Prob. 15CRECh. 1.CRE - Prob. 16CRECh. 1.CRE - Prob. 17CRECh. 1.CRE - Prob. 18CRECh. 1.CRE - Prob. 19CRECh. 1.CRE - Prob. 20CRECh. 1.CRE - Prob. 21CRECh. 1.CRE - Prob. 22CRECh. 1.CRE - Prob. 23CRECh. 1.CRE - Prob. 24CRECh. 1.CRE - Prob. 25CRECh. 1.CRE - Prob. 26CRECh. 1.CRE - PROFIT FUNCTION FOR DISPOSABLE CAMERAS A company...Ch. 1.CRE - Prob. 28CRECh. 1.CRE - Prob. 29CRECh. 1.CRE - Prob. 30CRECh. 1.CRE - SUPPLY EQUATION FOR BYCYCLES Bicycle suppliers...Ch. 1.CRE - DEMAND FOR EARBUD HEADPHONES The demand equation...Ch. 1.CRE - Prob. 33CRECh. 1.CRE - Prob. 34CRECh. 1.CRE - Prob. 35CRECh. 1.CRE - Prob. 36CRECh. 1.CRE - Prob. 37CRECh. 1.CRE - Prob. 38CRECh. 1.CRE - MARKET EQUILIBRIUM FOR REFRIGERATORS The demand...Ch. 1.CRE - Prob. 40CRECh. 1.CRE - EQUILIBRIUM QUANTITY AND PRICE FOR EARBUD...Ch. 1.CRE - Prob. 42CRECh. 1.BMO - Plot the points A(2,1) and B(3,4) on the same set...Ch. 1.BMO - Prob. 2BMOCh. 1.BMO - Prob. 3BMOCh. 1.BMO - Prob. 4BMOCh. 1.BMO - Prob. 5BMOCh. 1.BMO - Prob. 6BMO
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