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 1.5, Problem 42E
Write an equation that defines a rational function with a vertical asymptote at
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3.1 Limits
1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice.
x+3°
x+3*
x+3
(a) Is 5
(c) Does not exist
(b) is 6
(d) is infinite
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
Chapter 1 Solutions
Calculus For The Life Sciences
Ch. 1.1 - YOUR TURN Find the slope of the line through (1,5)...Ch. 1.1 - YOUR TURN Find the equation of the line with...Ch. 1.1 - Prob. 3YTCh. 1.1 - Prob. 4YTCh. 1.1 - Prob. 5YTCh. 1.1 - Prob. 6YTCh. 1.1 - Find the slope of each line. Through (4,5) and...Ch. 1.1 - Prob. 2ECh. 1.1 - Find the slope of each line. Through (8,4) and...Ch. 1.1 - Prob. 4E
Ch. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - Prob. 10ECh. 1.1 - Prob. 11ECh. 1.1 - Prob. 12ECh. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - In Exercises 15-24, find the equation in the...Ch. 1.1 - In Exercises 15-24, find the equation in the...Ch. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - In Exercises 15-24, find an equation in...Ch. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - In Exercises 25-34, find an equation for each line...Ch. 1.1 - In Exercises 25-34, find an equation for each line...Ch. 1.1 - In Exercises 25-34, find an equation for each line...Ch. 1.1 - In Exercises 25-34, find an equation for each line...Ch. 1.1 - In Exercises 25-34, find an equation for each line...Ch. 1.1 - In Exercises 25-34, find an equation for each line...Ch. 1.1 - In Exercises 25-34, find an equation for each line...Ch. 1.1 - In Exercises 25-34, find an equation for each line...Ch. 1.1 - Do the points (4,3), (2,0), and (18,12) lie on the...Ch. 1.1 - Find k so that the line through (4,1) and (k,2) is...Ch. 1.1 - Use slopes to show that the quadrilateral with...Ch. 1.1 - Use slopes to show that the square with vertices...Ch. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - In Exercises 41 and 42, estimate the slope of the...Ch. 1.1 - Prob. 43ECh. 1.1 - Prob. 44ECh. 1.1 - Prob. 45ECh. 1.1 - Prob. 46ECh. 1.1 - Graph each equation. y=4x+9Ch. 1.1 - Graph each equation. y=6x+12Ch. 1.1 - Graph each equation. 2x3y=12Ch. 1.1 - Graph each equation. 3xy=9Ch. 1.1 - Graph each equation. 3y7x=21Ch. 1.1 - Prob. 52ECh. 1.1 - Graph each equation. y=2Ch. 1.1 - Prob. 54ECh. 1.1 - Prob. 55ECh. 1.1 - Prob. 56ECh. 1.1 - Prob. 57ECh. 1.1 - Prob. 58ECh. 1.1 - Prob. 59ECh. 1.1 - Prob. 60ECh. 1.1 - Prob. 61ECh. 1.1 - Prob. 62ECh. 1.1 - Prob. 63ECh. 1.1 - Prob. 64ECh. 1.1 - For Exercises 6170, let f(x)=75xand g(x)=2x3. Find...Ch. 1.1 - Prob. 66ECh. 1.1 - Prob. 67ECh. 1.1 - Prob. 68ECh. 1.1 - Prob. 69ECh. 1.1 - Prob. 70ECh. 1.1 - LIFE SCIENCE APPLICATIONS Exercise Heart Rate To...Ch. 1.1 - LIFE SCIENCE APPLICATIONS HIV Infection The time...Ch. 1.1 - Life Expectancy Some scientists believe that there...Ch. 1.1 - Prob. 74ECh. 1.1 - Prob. 75ECh. 1.1 - Prob. 76ECh. 1.1 - Prob. 77ECh. 1.1 - Prob. 78ECh. 1.1 - Global Warming In 1990, the Intergovernmental...Ch. 1.1 - Body Temperature You may have heard that the...Ch. 1.1 - LIFE SCIENCE APPLICATIONS Cost Analysis Suppose a...Ch. 1.1 - LIFE SCIENCE APPLICATIONS Cost Analysis Acme...Ch. 1.1 - OTHER APPLICATIONS Marriage The following table...Ch. 1.1 - OTHER APPLICATIONS Immigration In 1950, there were...Ch. 1.1 - OTHER APPLICATIONS Child Mortality Rate The...Ch. 1.1 - Prob. 86ECh. 1.1 - Prob. 87ECh. 1.2 - YOUR TURN 1 Calculate the least squares line for...Ch. 1.2 - Prob. 2YTCh. 1.2 - Prob. 1ECh. 1.2 - Prob. 2ECh. 1.2 - For the following table of data. x 1 2 3 4 5 6 7 8...Ch. 1.2 - Prob. 4ECh. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - LIFE SCIENCE APPLICATIONS Bird Eggs The average...Ch. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - LIFE SCIENCE APPLICATIONS Length of a Pendulum...Ch. 1.2 - Prob. 22ECh. 1.3 - YOUR TURN Find the domain and range for the...Ch. 1.3 - Prob. 2YTCh. 1.3 - YOUR TURN Given the function f(x)=3x+6 and...Ch. 1.3 - Prob. 1ECh. 1.3 - Prob. 2ECh. 1.3 - Which of the following rules define y as a...Ch. 1.3 - Which of the following rules define y as a...Ch. 1.3 - Which of the following rules define y as a...Ch. 1.3 - Which of the following rules define y as a...Ch. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain of each function defined as...Ch. 1.3 - Give the domain and range of each function. Where...Ch. 1.3 - Give the domain and range of each function. Where...Ch. 1.3 - Give the domain and the range of each function....Ch. 1.3 - Give the domain and the range of each function....Ch. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - In Exercises 3740, give the domain and range....Ch. 1.3 - In Exercises 3740, give the domain and range....Ch. 1.3 - For each function, find (a) , (b) , (c) , (d) ,...Ch. 1.3 - For each function, find a f(4), b f(-1/2), c f(a),...Ch. 1.3 - For each function, find a f(4), b f(-1/2), c f(a),...Ch. 1.3 - For each function, find (a) , (b) , (c) , (d) ,...Ch. 1.3 - Let f(x)=6x2-2and g(x)=x2-2x+5to find the...Ch. 1.3 - Let f(x)=6x2-2and g(x)=x2-2x+5to find the...Ch. 1.3 - Let f(x)=6x2-2and g(x)=x2-2x+5to find the...Ch. 1.3 - Let f(x)=6x2-2and g(x)=x2-2x+5to find the...Ch. 1.3 - Let f(x)=6x22 and g(x)=x22x+5to find the following...Ch. 1.3 - Let f(x)=6x22 and g(x)=x22x+5to find the following...Ch. 1.3 - For each function defined as follows, find...Ch. 1.3 - For each function defined as follows, find...Ch. 1.3 - For each function defined as follows, find...Ch. 1.3 - For each function defined as follows, find...Ch. 1.3 - For each function defined as follows, find...Ch. 1.3 - For each function defined as follows, find...Ch. 1.3 - Decide whether each graph represents a function.Ch. 1.3 - Decide whether each graph represents a function.Ch. 1.3 - Decide whether each graph represents a function.Ch. 1.3 - Decide whether each graph represents a function.Ch. 1.3 - Decide whether each graph represents a function.Ch. 1.3 - Decide whether each graph represents a function.Ch. 1.3 - For each pair of functions, find a f(g(1)), b...Ch. 1.3 - For each pair of functions, find a f(g(1)), b...Ch. 1.3 - For each pair of functions, find a f(g(1)), b...Ch. 1.3 - For each pair of functions, find a f(g(1)), b...Ch. 1.3 - LIFE SCIENCE APPLICATIONS Whales Diving The figure...Ch. 1.3 - LIFE SCIENCE APPLICATIONS Metabolic Rate The basal...Ch. 1.3 - LIFE SCIENCE APPLICATIONS Swimming Energy The...Ch. 1.3 - OTHER APPLICATIONS Perimeter A rectangular field...Ch. 1.3 - OTHER APPLICATIONS Area A rectangular field is to...Ch. 1.3 - Prob. 72ECh. 1.3 - Prob. 73ECh. 1.4 - YOUR TURN For the function y=2x26x1, (a) complete...Ch. 1.4 - YOUR TURN Graph each of the following: (a)...Ch. 1.4 - How does the value of a affect the graph of y=ax2?...Ch. 1.4 - Prob. 2ECh. 1.4 - In Exercises 3-8, match the correct graph A-F to...Ch. 1.4 - In Exercises 3-8, match the correct graph A-F to...Ch. 1.4 - In Exercises 3-8, match the correct graph A-F to...Ch. 1.4 - In Exercises 3-8, match the correct graph A-F to...Ch. 1.4 - In Exercises 3-8, match the correct graph A-F to...Ch. 1.4 - In Exercises 3-8, match the correct graph A-F to...Ch. 1.4 - Complete the square and determine the vertex for...Ch. 1.4 - Complete the square and determine the vertex for...Ch. 1.4 - Complete the square and determine the vertex for...Ch. 1.4 - Complete the square and determine the vertex for...Ch. 1.4 - In Exercises 13-24, graph each parabola and give...Ch. 1.4 - In Exercises 13-24, graph each parabola and give...Ch. 1.4 - In Exercises 13-24, graph each parabola and give...Ch. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1.4 - Use the ideas in this section to graph each...Ch. 1.4 - Use the ideas in this section to graph each...Ch. 1.4 - Use the ideas in this section to graph each...Ch. 1.4 - Prob. 38ECh. 1.4 - Prob. 39ECh. 1.4 - Prob. 40ECh. 1.4 - Prob. 41ECh. 1.4 - Using the graph of f(x) in Figure 40, show the...Ch. 1.4 - Using the graph of f(x) in Figure 40, show the...Ch. 1.4 - Prob. 44ECh. 1.4 - Using the graph of f(x) in Figure 40, show the...Ch. 1.4 - If r is an x-intercept of the graph of y=f(x),...Ch. 1.4 - If b is the y-intercept of the graph of y=f(x),...Ch. 1.4 - LIFE SCIENCE APPLICATIONS Length of Life According...Ch. 1.4 - LIFE SCIENCE APPLICATIONS Tooth Length The length...Ch. 1.4 - LIFE SCIENCE APPLICATIONS APPLY IT Splenic Artery...Ch. 1.4 - Prob. 52ECh. 1.4 - LIFE SCIENCE APPLICATIONS Gender Ratio The number...Ch. 1.4 - Prob. 54ECh. 1.4 - OTHER APPLICATIONS Accident Rate According to data...Ch. 1.4 - OTHER APPLICATIONS Maximizing the Height of an...Ch. 1.4 - OTHER APPLICATIONS Stopping Distance According to...Ch. 1.4 - Prob. 59ECh. 1.4 - OTHER APPLICATIONS Maximizing Area What would be...Ch. 1.4 - Prob. 61ECh. 1.4 - OTHER APPLICATIONS In Exercises 61 and 62, draw a...Ch. 1.5 - YOUR TURN 1 Graph f(x)=64x6.Ch. 1.5 - Prob. 1ECh. 1.5 - Describe an asymptote, and explain when a rational...Ch. 1.5 - Use the principles of the previous section with...Ch. 1.5 - Use the principles of the previous section with...Ch. 1.5 - Prob. 5ECh. 1.5 - Prob. 6ECh. 1.5 - EXERCISES In Exercises 7-15, match the correct...Ch. 1.5 - EXERCISES In Exercises 7-15, match the correct...Ch. 1.5 - EXERCISES In Exercises 7-15, match the correct...Ch. 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 - EXERCISES In Exercises 16-20, match the correct...Ch. 1.5 - EXERCISES In Exercises 16-20, match the correct...Ch. 1.5 - Prob. 21ECh. 1.5 - Prob. 22ECh. 1.5 - Prob. 23ECh. 1.5 - Prob. 24ECh. 1.5 - Prob. 25ECh. 1.5 - Prob. 26ECh. 1.5 - Prob. 27ECh. 1.5 - Prob. 29ECh. 1.5 - Prob. 30ECh. 1.5 - Prob. 31ECh. 1.5 - Prob. 32ECh. 1.5 - Prob. 33ECh. 1.5 - Prob. 34ECh. 1.5 - Prob. 35ECh. 1.5 - Prob. 36ECh. 1.5 - Prob. 37ECh. 1.5 - Find any horizontal and vertical asymptotes and...Ch. 1.5 - Prob. 39ECh. 1.5 - Prob. 40ECh. 1.5 - Prob. 41ECh. 1.5 - Write an equation that defines a rational function...Ch. 1.5 - Prob. 43ECh. 1.5 - Prob. 44ECh. 1.5 - Prob. 45ECh. 1.5 - Prob. 46ECh. 1.5 - LIFE SCIENCE APPLICATIONS Alcohol Concentration...Ch. 1.5 - Prob. 48ECh. 1.5 - Prob. 49ECh. 1.5 - Prob. 50ECh. 1.5 - Prob. 51ECh. 1.5 - Prob. 52ECh. 1.5 - Prob. 53ECh. 1.5 - Prob. 54ECh. 1.5 - Prob. 55ECh. 1.5 - Prob. 56ECh. 1.5 - Prob. 57ECh. 1.5 - OTHER APPLICATIONS Length of a Pendulum. A simple...Ch. 1.5 - Prob. 59ECh. 1.CR - Concept Check Determine whether each statement is...Ch. 1.CR - Prob. 2CRCh. 1.CR - Prob. 3CRCh. 1.CR - Prob. 4CRCh. 1.CR - Prob. 5CRCh. 1.CR - Prob. 6CRCh. 1.CR - Prob. 7CRCh. 1.CR - Prob. 8CRCh. 1.CR - Prob. 9CRCh. 1.CR - Prob. 10CRCh. 1.CR - CONCEPT CHECK Determine whether each statement is...Ch. 1.CR - Prob. 12CRCh. 1.CR - Prob. 13CRCh. 1.CR - CONCEPT CHECK Determine whether each statement is...Ch. 1.CR - Prob. 15CRCh. 1.CR - Prob. 16CRCh. 1.CR - Prob. 17CRCh. 1.CR - Prob. 18CRCh. 1.CR - Prob. 19CRCh. 1.CR - Prob. 20CRCh. 1.CR - Prob. 21CRCh. 1.CR - Prob. 22CRCh. 1.CR - Prob. 23CRCh. 1.CR - Prob. 24CRCh. 1.CR - Prob. 25CRCh. 1.CR - Prob. 26CRCh. 1.CR - Prob. 27CRCh. 1.CR - Prob. 28CRCh. 1.CR - Prob. 29CRCh. 1.CR - Prob. 30CRCh. 1.CR - Prob. 31CRCh. 1.CR - Prob. 32CRCh. 1.CR - Prob. 33CRCh. 1.CR - Prob. 34CRCh. 1.CR - Prob. 35CRCh. 1.CR - Prob. 36CRCh. 1.CR - Prob. 37CRCh. 1.CR - Prob. 38CRCh. 1.CR - Prob. 39CRCh. 1.CR - Prob. 40CRCh. 1.CR - Prob. 41CRCh. 1.CR - Prob. 42CRCh. 1.CR - Prob. 43CRCh. 1.CR - Prob. 44CRCh. 1.CR - Prob. 45CRCh. 1.CR - PRACTICE AND EXPLORATIONS Find an equation for...Ch. 1.CR - Prob. 47CRCh. 1.CR - Prob. 48CRCh. 1.CR - Prob. 49CRCh. 1.CR - Prob. 50CRCh. 1.CR - Prob. 51CRCh. 1.CR - Prob. 52CRCh. 1.CR - Prob. 53CRCh. 1.CR - Prob. 54CRCh. 1.CR - Prob. 55CRCh. 1.CR - Prob. 56CRCh. 1.CR - Prob. 57CRCh. 1.CR - Prob. 58CRCh. 1.CR - Prob. 59CRCh. 1.CR - Prob. 60CRCh. 1.CR - Prob. 61CRCh. 1.CR - Prob. 62CRCh. 1.CR - Prob. 63CRCh. 1.CR - Prob. 64CRCh. 1.CR - Prob. 65CRCh. 1.CR - Prob. 66CRCh. 1.CR - Prob. 67CRCh. 1.CR - Prob. 68CRCh. 1.CR - Prob. 69CRCh. 1.CR - Prob. 70CRCh. 1.CR - Prob. 71CRCh. 1.CR - Prob. 72CRCh. 1.CR - Prob. 73CRCh. 1.CR - Prob. 74CRCh. 1.CR - Prob. 75CRCh. 1.CR - Prob. 76CRCh. 1.CR - Prob. 77CRCh. 1.CR - Prob. 78CRCh. 1.CR - Prob. 79CRCh. 1.CR - Prob. 80CRCh. 1.CR - Prob. 81CRCh. 1.CR - Prob. 82CRCh. 1.CR - Prob. 83CRCh. 1.CR - Prob. 84CRCh. 1.CR - Prob. 85CRCh. 1.CR - Prob. 86CRCh. 1.CR - Prob. 87CRCh. 1.CR - Prob. 88CRCh. 1.CR - Prob. 91CRCh. 1.CR - Prob. 92CRCh. 1.CR - OTHER APPLICATIONS Planets The following table...Ch. 1.EA - Prob. 1EACh. 1.EA - Prob. 2EACh. 1.EA - Prob. 3EACh. 1.EA - EXERCISES The following table gives the life...Ch. 1.EA - Prob. 5EACh. 1.EA - Prob. 6EACh. 1.EA - Prob. 7EACh. 1.EA - Prob. 8EA
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