Calculus For The Life Sciences
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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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 7.1, Problem 61E

Rocket A small rocket was launched straight up from a platform. After 5 seconds, the rocket reached a maximum height of 412   ft . Find the initial velocity and height of the rocket. (Hint: See previous exercise.)

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Chapter 7 Solutions

Calculus For The Life Sciences

Ch. 7.1 - YOUR TURN Find an antiderivative of f(x)=8x7.Ch. 7.1 - Prob. 2YTCh. 7.1 - Prob. 3YTCh. 7.1 - Prob. 4YTCh. 7.1 - Prob. 5YTCh. 7.1 - Prob. 6YTCh. 7.1 - YOUR TURN Find an equation of the curve whose...Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3E
Ch. 7.1 - Explain why the restriction n1 is necessary in the...Ch. 7.1 - Prob. 5ECh. 7.1 - Find the following. 9dyCh. 7.1 - Find the following. (2z+3)dzCh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10ECh. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Find the following. x2(x4+4x+3)dxCh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Find the following. (56t5/2+18t7/2)dtCh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Find the following. 13x2dxCh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Find the following. (3x+4e0.4+eo.1)dxCh. 7.1 - Find the following. (9x3e0.4x)dxCh. 7.1 - Prob. 33ECh. 7.1 - Find the following. 2y1/23y26ydyCh. 7.1 - Prob. 35ECh. 7.1 - Find the following. (v2e3v)dvCh. 7.1 - Prob. 37ECh. 7.1 - Find the following. (2y1)2dyCh. 7.1 - Find the following. x+1x3dxCh. 7.1 - Find the following. 12z3z3dzCh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Find the following. (3cosx4sinx)dxCh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - The slope of the tangent line to a curve is given...Ch. 7.1 - LIFE SCIENCE APPLICATIONS Biochemical Excretion If...Ch. 7.1 - LIFE SCIENCE APPLICATIONS Flour Beetles A model...Ch. 7.1 - Concentration of a solute According to the Ficks...Ch. 7.1 - Cell Growth Under certain conditions, the number...Ch. 7.1 - Blood Pressure The rate of change of the volume...Ch. 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 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Motion under gravityShow that an object thrown...Ch. 7.1 - Rocket A small rocket was launched straight up...Ch. 7.1 - Rocket science In the 1999 movie October Sky,...Ch. 7.2 - YOUR TURN Find 8x(4x2+8)6dx.Ch. 7.2 - YOUR TURN Find x33x4+10dx.Ch. 7.2 - YOUR TURN Find x+1(4x2+8x)3dx.Ch. 7.2 - YOUR TURN Find x+3x2+6xdx.Ch. 7.2 - YOUR TURN Find x3ex4dx.Ch. 7.2 - Prob. 6YTCh. 7.2 - Prob. 7YTCh. 7.2 - Prob. 8YTCh. 7.2 - Integration by substitution is related to what...Ch. 7.2 - The following integrals may be solved using...Ch. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 4ECh. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 10ECh. 7.2 - Prob. 11ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 16ECh. 7.2 - Prob. 17ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 25ECh. 7.2 - Use substitution to find the indefinite integral....Ch. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 30ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 48ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 56ECh. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - Stan and Ollie work on the integral 2x(x2+2)dx....Ch. 7.2 - Outpatient Visits According to the data from the...Ch. 7.2 - Prob. 62ECh. 7.2 - Prob. 63ECh. 7.2 - Prob. 64ECh. 7.2 - Prob. 65ECh. 7.2 - Prob. 66ECh. 7.2 - Prob. 67ECh. 7.3 - YOUR TURN 1 Repeat Example 1 to approximate...Ch. 7.3 - Prob. 2YTCh. 7.3 - Explain the difference between an indefinite...Ch. 7.3 - Complete the following statement. 04(x2+3)dx=limn,...Ch. 7.3 - Let f(x)=2x+5, x1=0, x2=2, x3=4, x4=6, and x=2. a....Ch. 7.3 - Let f(x)=1/x, x1=1/2, x2=1, x3=3/2, x4=2, and...Ch. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - In Exercise 5-14, approximate the area under the...Ch. 7.3 - Prob. 11ECh. 7.3 - In Exercise 5-14, approximate the area under the...Ch. 7.3 - In Exercise 5-14, approximate the area under the...Ch. 7.3 - Prob. 14ECh. 7.3 - Consider the region below f(x)=x/2, above the...Ch. 7.3 - Consider the region below f(x)=5x, above the...Ch. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - In Exercises 2631, estimate the area under each...Ch. 7.3 - APPLY IT Foot-and-Mouth Epidemic In 2001, the...Ch. 7.3 - In Exercises 2631, estimate the area under each...Ch. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - DistanceWhen data are given in tabular form, you...Ch. 7.3 - Heat Gain The following graphs show the typical...Ch. 7.3 - Heat Gain The following graphs show the typical...Ch. 7.3 - Automobile VelocityTwo cars start from rest at a...Ch. 7.3 - Distance Musk the friendly pit bull has escaped...Ch. 7.3 - Distance The speed of a particle in a test...Ch. 7.3 - Running In 1987, Canadian Ben Johnson set a world...Ch. 7.3 - Traffic The following graph shows the number of...Ch. 7.4 - YOUR TURN Find 133x2dx.Ch. 7.4 - Prob. 2YTCh. 7.4 - Prob. 3YTCh. 7.4 - Prob. 4YTCh. 7.4 - Prob. 5YTCh. 7.4 - YOUR TURN Find the area under the curve...Ch. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.4 - Evaluate each definite integral. 12(5t3)dtCh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Evaluate each definite integral. 23(x23x+5)dxCh. 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 - Evaluate each definite integral. 143(2p+1)2dpCh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Evaluate each definite integral. 10y(2y23)5dyCh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Evaluate each definite integral. 0/4sinxdxCh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Evaluate each definite integral. /22/3cosxdxCh. 7.4 - Prob. 36ECh. 7.4 - In Exercises 37-48, use the definite integral to...Ch. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - In Exercises 37-48, use the definite integral to...Ch. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - In Exercises 37-48, use the definite integral to...Ch. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Find the area of each shaded region.Ch. 7.4 - Prob. 52ECh. 7.4 - Assume f(x) is continuous for gxc, as shown in the...Ch. 7.4 - Is the equation you wrote for Exercise 53 still...Ch. 7.4 - The graph of f(x), shown here, consists of two...Ch. 7.4 - Use the Fundamental Theorem to show that the...Ch. 7.4 - Use the Fundamental Theorem to show that the...Ch. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - You are given 01ex2dx=1.46265 and...Ch. 7.4 - Let g(t)=t4 and define f(x)=cxg(t)dt with c=1. a....Ch. 7.4 - Prob. 62ECh. 7.4 - LIFE SCIENCE APPLICATIONS Pollution Pollution from...Ch. 7.4 - LIFE SCIENCE APPLICATIONS Spread of an Oil Leak An...Ch. 7.4 - LIFE SCIENCE APPLICATIONS Tree Growth After long...Ch. 7.4 - LIFE SCIENCE APPLICATIONS Growth of a SubstanceThe...Ch. 7.4 - LIFE SCIENCE APPLICATIONS Drug Reaction For a...Ch. 7.4 - LIFE SCIENCE APPLICATIONS Human Mortality If f(x)...Ch. 7.4 - Cell Division Let the expected number of cells in...Ch. 7.4 - LIFE SCIENCE APPLICATIONS Bacterial Growth A...Ch. 7.4 - Prob. 71ECh. 7.4 - Prob. 72ECh. 7.4 - Sediment The density of sediment in grams per...Ch. 7.4 - Prob. 75ECh. 7.4 - Prob. 76ECh. 7.4 - Biochemical Reaction In an example of the...Ch. 7.4 - Prob. 78ECh. 7.4 - Prob. 79ECh. 7.4 - Prob. 80ECh. 7.4 - Prob. 81ECh. 7.4 - Oil Consumption Suppose that the rate of...Ch. 7.4 - Prob. 83ECh. 7.4 - Prob. 85ECh. 7.5 - Prob. 1YTCh. 7.5 - Prob. 2YTCh. 7.5 - Prob. 3YTCh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 11ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.5 - Prob. 19ECh. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 24ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 28ECh. 7.5 - Prob. 29ECh. 7.5 - Prob. 30ECh. 7.5 - LIFE SCIENCE APPLICATIONS Pollution Pollution...Ch. 7.5 - OTHER APPLICATIONS Distribution of Income Suppose...Ch. 7.5 - OTHER APPLICATIONS Net SavingsSuppose a company...Ch. 7.5 - Prob. 36ECh. 7.5 - ProfitCanham Enterprises had an expenditure rate...Ch. 7.5 - Net SavingsA factory of Hollis Sherman Industries...Ch. 7.CR - CONCEPT CHECK Determine whether each of the...Ch. 7.CR - Prob. 2CRCh. 7.CR - Prob. 3CRCh. 7.CR - Prob. 4CRCh. 7.CR - CONCEPT CHECK Determine whether each of the...Ch. 7.CR - Prob. 6CRCh. 7.CR - Prob. 7CRCh. 7.CR - Prob. 8CRCh. 7.CR - Prob. 9CRCh. 7.CR - Prob. 10CRCh. 7.CR - Prob. 11CRCh. 7.CR - Prob. 12CRCh. 7.CR - Prob. 13CRCh. 7.CR - Prob. 14CRCh. 7.CR - Prob. 15CRCh. 7.CR - Prob. 16CRCh. 7.CR - Prob. 17CRCh. 7.CR - Prob. 18CRCh. 7.CR - Prob. 19CRCh. 7.CR - Prob. 20CRCh. 7.CR - Prob. 21CRCh. 7.CR - Prob. 22CRCh. 7.CR - Prob. 23CRCh. 7.CR - Prob. 24CRCh. 7.CR - Prob. 25CRCh. 7.CR - Prob. 26CRCh. 7.CR - Prob. 27CRCh. 7.CR - Prob. 28CRCh. 7.CR - Prob. 29CRCh. 7.CR - Prob. 30CRCh. 7.CR - Prob. 31CRCh. 7.CR - Prob. 32CRCh. 7.CR - Prob. 33CRCh. 7.CR - Prob. 34CRCh. 7.CR - Prob. 35CRCh. 7.CR - Prob. 36CRCh. 7.CR - Prob. 37CRCh. 7.CR - Prob. 38CRCh. 7.CR - Prob. 39CRCh. 7.CR - Prob. 40CRCh. 7.CR - Prob. 41CRCh. 7.CR - Prob. 42CRCh. 7.CR - Prob. 43CRCh. 7.CR - Prob. 44CRCh. 7.CR - Prob. 45CRCh. 7.CR - Prob. 46CRCh. 7.CR - Prob. 47CRCh. 7.CR - Prob. 48CRCh. 7.CR - Prob. 49CRCh. 7.CR - Prob. 50CRCh. 7.CR - Prob. 51CRCh. 7.CR - Prob. 52CRCh. 7.CR - Find 04f(x)dx for each graph of y=f(x). a.b.Ch. 7.CR - Prob. 54CRCh. 7.CR - Prob. 55CRCh. 7.CR - In Exercises 32 and 33 of Section 7.3 on Area and...Ch. 7.CR - Prob. 57CRCh. 7.CR - Prob. 58CRCh. 7.CR - Prob. 59CRCh. 7.CR - Prob. 60CRCh. 7.CR - Prob. 61CRCh. 7.CR - Prob. 62CRCh. 7.CR - Prob. 63CRCh. 7.CR - Prob. 64CRCh. 7.CR - Prob. 65CRCh. 7.CR - Prob. 66CRCh. 7.CR - Prob. 67CRCh. 7.CR - Prob. 68CRCh. 7.CR - Prob. 69CRCh. 7.CR - Prob. 70CRCh. 7.CR - Prob. 71CRCh. 7.CR - Prob. 72CRCh. 7.CR - Prob. 73CRCh. 7.CR - Prob. 74CRCh. 7.CR - Prob. 75CRCh. 7.CR - Prob. 76CRCh. 7.CR - Prob. 77CRCh. 7.CR - Prob. 78CRCh. 7.CR - Prob. 79CRCh. 7.CR - Prob. 80CRCh. 7.CR - Prob. 81CRCh. 7.CR - LIFE SCIENCE APPLICATIONS Population GrowthThe...Ch. 7.CR - LIFE SCIENCE APPLICATIONS Infection Rate The rate...Ch. 7.CR - Insect CannibalismIn certain species of flour...Ch. 7.CR - Risk in Fisheries We saw in the previous chapter...Ch. 7.CR - Oil ProductionThe following table shows the amount...Ch. 7.CR - Prob. 88CRCh. 7.CR - Prob. 89CRCh. 7.CR - Energy ConsumptionThe monthly residential...Ch. 7.CR - TemperatureThe table lists the average monthly...Ch. 7.CR - Net SavingsA company has installed new machinery...Ch. 7.EA - Prob. 1EACh. 7.EA - Prob. 2EACh. 7.EA - Prob. 3EACh. 7.EA - Prob. 4EACh. 7.EA - Prob. 5EACh. 7.EA - Prob. 6EA
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