EBK CALCULUS FOR THE LIFE SCIENCES
EBK CALCULUS FOR THE LIFE SCIENCES
2nd Edition
ISBN: 9780321964458
Author: Lial
Publisher: PEARSON EDUCATION (COLLEGE)
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Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 1.1, Problem 74E
To determine

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The speed at which the pony switched from a trot to a gallop.

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7) 8) Let R be the region bounded by the given curves as shown in the figure. If the line x = k divides R into two regions of equal area, find the value of k 7. y = 3√x, y = √x and x = 4 8. y = -2, y = 3, x = −3, and x = −1 -1 2 +1 R R
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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 1 Solutions

EBK 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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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY