Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Textbook Question
Chapter 4.6, Problem 32E
In Exercises 27-32, recall that the slope of the tangent line to a graph is given by the derivative of the function. Find the slope of the tangent line to the graph of each equation at the given point. You may wish to use a graphing calculator to support your answers.
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Chapter 4 Solutions
Calculus For The Life Sciences
Ch. 4.1 - YOUR TURN If ft=1t, find f't.Ch. 4.1 - Prob. 2YTCh. 4.1 - YOUR TURN If ht=-3t2+2t+5t4-7, find h't.Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...
Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Which of the following describes the derivative...Ch. 4.1 - Which of the following describes the derivative...Ch. 4.1 - Explain the relationship between the slope and the...Ch. 4.1 - Prob. 26ECh. 4.1 - Find each derivative. Dx9x-1/2+2x3/2Ch. 4.1 - Find each derivative. Dx8x4-3x3Ch. 4.1 - Prob. 29ECh. 4.1 - Find each derivative. f'3 if fx=x39-7x2Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - Prob. 35ECh. 4.1 - Find all points on the graph of fx=x3+9x2+19x-10...Ch. 4.1 - Prob. 37ECh. 4.1 - In Exercises 37-40, for each function find all...Ch. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - At what point on the graph of fx=-5x2+4x-2 is the...Ch. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - In Exercises 43-46 of section 1.4, the effect of a...Ch. 4.1 - Show that, for any constant k, ddxfxk=f'xk.Ch. 4.1 - Prob. 50ECh. 4.1 - Cancer Insulation workers who were exposed to...Ch. 4.1 - Prob. 52ECh. 4.1 - Insect Mating Patterns In an experiment testing...Ch. 4.1 - Prob. 54ECh. 4.1 - Bighorn Sheep The cumulative horn volume for...Ch. 4.1 - Brain Mass The brain mass of a human fetus during...Ch. 4.1 - Prob. 57ECh. 4.1 - Body Mass Index The body mass index BMI is a...Ch. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Dogs Human Age From the data printed in the...Ch. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Postal Rates U.S postal rates have steadily...Ch. 4.1 - Money The total amount of money in circulation for...Ch. 4.1 - Prob. 75ECh. 4.2 - YOUR TURN Find the derivative of y=x3+74-x2.Ch. 4.2 - Prob. 2YTCh. 4.2 - YOUR TURN Find Dx5x-32x+73x+7.Ch. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 26ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Find the error in the following work....Ch. 4.2 - Prob. 32ECh. 4.2 - Find an equation of the line tangent to the graph...Ch. 4.2 - Find an equation of the line tangent to the graph...Ch. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - For each function, find the values of x in which...Ch. 4.2 - Prob. 41ECh. 4.2 - Growth Models In Exercise 52 of section 1.5, the...Ch. 4.2 - Bacteria Population Assume that the total number...Ch. 4.2 - Work/Rest Cycles Murrells formula for calculating...Ch. 4.2 - Optimal Foraging Using data collected by zoologist...Ch. 4.2 - Cell Traction Force In a matrix of cells, the cell...Ch. 4.2 - Prob. 47ECh. 4.2 - Cellular Chemistry The release of a chemical...Ch. 4.2 - Prob. 49ECh. 4.2 - Memory Retention Some psychologists content that...Ch. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.3 - YOUR TURN For the functions in Example 1, find fg0...Ch. 4.3 - YOUR TURN Let fx=2x-3 and gx=x2+1. Find gfx.Ch. 4.3 - YOUR TURN Write hx=2x-33 as a composition of two...Ch. 4.3 - YOUR TURN Find dy/dx if y=5x2-6x-2.Ch. 4.3 - Prob. 5YTCh. 4.3 - Prob. 6YTCh. 4.3 - Prob. 7YTCh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - In Exercises 7-14, find f[gx] and g[fx]. fx=x+2;...Ch. 4.3 - In Exercises 7-14, find f[gx] and g[fx]....Ch. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Write each function as the composition of two...Ch. 4.3 - Prob. 21ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 23ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Consider the following table of values of the...Ch. 4.3 - Prob. 45ECh. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Katie and Sarah are working on taking the...Ch. 4.3 - Margy and Nate are working on taking the...Ch. 4.3 - Prob. 53ECh. 4.3 - Oil Pollution An oil well off the Gulf Coast is...Ch. 4.3 - African Wild Dog The African wild dog is currently...Ch. 4.3 - Thermal Inversion When there is a thermal...Ch. 4.3 - Prob. 57ECh. 4.3 - Calcium Usage To test an individuals use of...Ch. 4.3 - Drug Reaction The strength of a persons reaction...Ch. 4.3 - Extinction The probability of a population going...Ch. 4.3 - Candy The volume and surface area of a jawbreaker...Ch. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.4 - YOUR TURN 1 Find dy/dx for a. y=43x, b. y=e7x3+5Ch. 4.4 - Prob. 2YTCh. 4.4 - Prob. 3YTCh. 4.4 - YOUR TURN 4 The quantity in grams of a radioactive...Ch. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 25ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 31ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 33ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Use graphical differentiation to verify that...Ch. 4.4 - Prob. 38ECh. 4.4 - Population Growth In section 2.1, Exercise 37, the...Ch. 4.4 - Minority Population In Section 2.1, Exercise 39,...Ch. 4.4 - Insect Growth The growth of a population of rare...Ch. 4.4 - Prob. 43ECh. 4.4 - Whooping Cranes Based on data from the U.S. Fish...Ch. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.4 - Mortality The percentage of people of any...Ch. 4.4 - Breast Cancer It has been observed that the...Ch. 4.4 - Arctic Foxes The age-weight relationship of female...Ch. 4.4 - Prob. 50ECh. 4.4 - Ayrshire Dairy Cattle The researchers from the...Ch. 4.4 - Cutlassfish The cutlassfish is one of the most...Ch. 4.4 - Prob. 53ECh. 4.4 - Dialysis One measure of whether a dialysis patient...Ch. 4.4 - Medical Literature It has been observed that there...Ch. 4.4 - Prob. 56ECh. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Radioactive Iron Researchers found that the...Ch. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Habit Strength According to work by the...Ch. 4.4 - Prob. 66ECh. 4.4 - Electricity In a series resistance-capacitance DC...Ch. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.5 - YOUR TURN Find the derivative of fx=log3x.Ch. 4.5 - Prob. 2YTCh. 4.5 - Prob. 3YTCh. 4.5 - Find the derivative of each function. y=ln8xCh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Find the derivative of each function. y=ln4x2-9xCh. 4.5 - Find the derivative of each function. y=ln-8x3+2xCh. 4.5 - Find the derivative of each function. y=lnx+5Ch. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Find the derivative of each function. y=xln2-x2Ch. 4.5 - Prob. 15ECh. 4.5 - Find the derivative of each function. v=lnuu3Ch. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Find the derivative of each function. y=3x2lnxCh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Find the derivative of each function. y=lnx-3Ch. 4.5 - Find the derivative of each function. y=lnlnxCh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Find the derivative of each function. py=lnyeyCh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Find the derivative of each function. y=log4x-3Ch. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Find the derivative of each function. y=log74x-3Ch. 4.5 - Find the derivative of each function....Ch. 4.5 - Find the derivative of each function....Ch. 4.5 - Prob. 39ECh. 4.5 - Find the derivative of each function. z=10ylogyCh. 4.5 - Prob. 41ECh. 4.5 - Find the derivative of each function. fx=lnxex+2Ch. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Use a graphing calculator to sketch the graph of...Ch. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - This exercise shows another way to derive the...Ch. 4.5 - Prob. 57ECh. 4.5 - Population Growth Suppose that the population of a...Ch. 4.5 - Body Surface Area There is a mathematical...Ch. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Fruit Flies A study of the relation between the...Ch. 4.5 - Prob. 63ECh. 4.5 - Poverty The passage of the Social Security...Ch. 4.5 - Richter Scale The Richter scale provides a measure...Ch. 4.5 - Prob. 66ECh. 4.6 - YOUR TURN Find the derivative of y=5sin3x4.Ch. 4.6 - YOUR TURN Find the derivative of y=2sin3x.Ch. 4.6 - Prob. 3YTCh. 4.6 - Prob. 4YTCh. 4.6 - Prob. 5YTCh. 4.6 - Prob. 6YTCh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 4ECh. 4.6 - Prob. 5ECh. 4.6 - Prob. 6ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 8ECh. 4.6 - Prob. 9ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 11ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 13ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 15ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 17ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 19ECh. 4.6 - Prob. 20ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 23ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 25ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - Prob. 29ECh. 4.6 - In Exercises 27-32, recall that the slope of the...Ch. 4.6 - Prob. 31ECh. 4.6 - In Exercises 27-32, recall that the slope of the...Ch. 4.6 - Find the derivative of cotx by using the quotient...Ch. 4.6 - Prob. 34ECh. 4.6 - Verify that the derivative of cscx is -cscxcotx....Ch. 4.6 - Prob. 36ECh. 4.6 - Prob. 37ECh. 4.6 - Carbon Dioxide Levels At Barrow, Alaska,...Ch. 4.6 - Prob. 39ECh. 4.6 - Sound If a string with a fundamental frequency of...Ch. 4.6 - Prob. 41ECh. 4.6 - Revenue from Seasonal Merchandise The revenue...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Prob. 10CRCh. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Prob. 12CRCh. 4.CR - Prob. 13CRCh. 4.CR - Prob. 14CRCh. 4.CR - Prob. 15CRCh. 4.CR - Prob. 16CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 19CRCh. 4.CR - Prob. 20CRCh. 4.CR - Prob. 21CRCh. 4.CR - Prob. 22CRCh. 4.CR - Prob. 23CRCh. 4.CR - Prob. 24CRCh. 4.CR - Prob. 25CRCh. 4.CR - Prob. 26CRCh. 4.CR - Prob. 27CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 29CRCh. 4.CR - Prob. 30CRCh. 4.CR - Prob. 31CRCh. 4.CR - Prob. 32CRCh. 4.CR - Prob. 33CRCh. 4.CR - Prob. 34CRCh. 4.CR - Prob. 35CRCh. 4.CR - Prob. 36CRCh. 4.CR - Prob. 37CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 39CRCh. 4.CR - Prob. 40CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 42CRCh. 4.CR - Prob. 43CRCh. 4.CR - Prob. 44CRCh. 4.CR - Prob. 45CRCh. 4.CR - Prob. 46CRCh. 4.CR - Prob. 47CRCh. 4.CR - Prob. 48CRCh. 4.CR - Prob. 49CRCh. 4.CR - Prob. 50CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 52CRCh. 4.CR - Prob. 53CRCh. 4.CR - Prob. 54CRCh. 4.CR - Prob. 55CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 57CRCh. 4.CR - Prob. 58CRCh. 4.CR - Prob. 59CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 61CRCh. 4.CR - Prob. 62CRCh. 4.CR - Prob. 63CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 65CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 68CRCh. 4.CR - Consider the following table of values of the...Ch. 4.CR - Consider the following table of values of the...Ch. 4.CR - Prob. 71CRCh. 4.CR - Prob. 72CRCh. 4.CR - Find the slope of the tangent line to the given...Ch. 4.CR - Prob. 74CRCh. 4.CR - Prob. 75CRCh. 4.CR - Prob. 76CRCh. 4.CR - Prob. 77CRCh. 4.CR - Prob. 78CRCh. 4.CR - Prob. 79CRCh. 4.CR - Prob. 80CRCh. 4.CR - Prob. 81CRCh. 4.CR - Prob. 82CRCh. 4.CR - Prob. 83CRCh. 4.CR - Prob. 84CRCh. 4.CR - Prob. 85CRCh. 4.CR - Prob. 86CRCh. 4.CR - Prob. 87CRCh. 4.CR - Prob. 88CRCh. 4.CR - Prob. 89CRCh. 4.CR - Exponential Growth Suppose a population is growing...Ch. 4.CR - Logistic Growth Suppose a population can be...Ch. 4.CR - Fish The length of the monkeyface prickleback, a...Ch. 4.CR - Prob. 93CRCh. 4.CR - Prob. 94CRCh. 4.CR - Prob. 95CRCh. 4.CR - Prob. 96CRCh. 4.CR - Prob. 97CRCh. 4.CR - Prob. 98CRCh. 4.CR - Prob. 99CRCh. 4.CR - Prob. 100CRCh. 4.CR - Prob. 101CRCh. 4.EA - Suppose that a particular plot of land can sustain...Ch. 4.EA - Prob. 2EA
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