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,
bartleby

Concept explainers

Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
bartleby

Videos

Textbook Question
Book Icon
Chapter 9.1, Problem 1E

EXERCISES

Let f ( x , y ) = 2 x − 3 y + 5. Find the following.

a. f ( 2 , − 1 ) b. f ( − 4 , 1 )
c. f ( − 2 , − 3 ) d. f ( 0 , 8 )
Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 9.1, Problem 3YT
Next
Chapter 9.1, Problem 2E
Students have asked these similar questions
A 20 foot ladder rests on level ground; its head (top) is against a vertical wall. The bottom of the ladder begins by being 12 feet from the wall but begins moving away at the rate of 0.1 feet per second. At what rate is the top of the ladder slipping down the wall? You may use a calculator.
Explain the focus and reasons for establishment of 12.4.1(root test) and 12.4.2(ratio test)
use Integration by Parts to derive 12.6.1

Chapter 9 Solutions

Calculus For The Life Sciences

Ch. 9.1 - YOUR TURN For the function in Example 1, find...Ch. 9.1 - Prob. 2YTCh. 9.1 - Prob. 3YTCh. 9.1 - EXERCISES Let f(x,y)=2x3y+5.Find the following. a....Ch. 9.1 - Prob. 2ECh. 9.1 - EXERCISES Let h(x,y)=x2+2y2. Find the following....Ch. 9.1 - EXERCISES Let f(x,y)=9x+5ylogx. Find the...Ch. 9.1 - EXERCISES Let f(x,y)=ex+ln(x+y). Find the...Ch. 9.1 - EXERCISES Let f(x,y)=xex+y. Find the following. a....Ch. 9.1 - EXERCISES Let f(x,y)=xsin(x2y). Find the...
Ch. 9.1 - EXERCISES Let f(x,y)=ycos(x+y).Find the following....Ch. 9.1 - EXERCISES Graph the level curves in the first...Ch. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Match each equation in Exercise 2530with its graph...Ch. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Let f(x,y)=xyex2+y2. Use a graphing calculator or...Ch. 9.1 - The following table provides values of the...Ch. 9.1 - LIFE SCIENCE APPLICATIONS Life Span Researchers...Ch. 9.1 - LIFE SCIENCE APPLICATIONS Heat Loss The rate of...Ch. 9.1 - LIFE SCIENCE APPLICATIONS Body Surface Area The...Ch. 9.1 - LIFE SCIENCE APPLICATIONS Dinosaur Running An...Ch. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Agriculture Pregnant sows tethered in stalls often...Ch. 9.1 - Prob. 44ECh. 9.1 - Total Body Water Accurate prediction of total body...Ch. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.2 - YOUR TURN Let f(x,y)=2x2y3+6x5y4. Find fx(x,y) and...Ch. 9.2 - Prob. 2YTCh. 9.2 - Prob. 3YTCh. 9.2 - Prob. 4YTCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - In Exercise 3-22 find fx(x,y)and fy(x,y).Then find...Ch. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - Prob. 45ECh. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - LIFE SCIENCE APPLICATIONS Calorie Expenditure The...Ch. 9.2 - Prob. 50ECh. 9.2 - Prob. 52ECh. 9.2 - Prob. 53ECh. 9.2 - Prob. 54ECh. 9.2 - Prob. 55ECh. 9.2 - Prob. 57ECh. 9.2 - Prob. 58ECh. 9.2 - Prob. 59ECh. 9.2 - Prob. 60ECh. 9.2 - Prob. 62ECh. 9.2 - Prob. 63ECh. 9.2 - Prob. 66ECh. 9.2 - Prob. 67ECh. 9.2 - Prob. 68ECh. 9.2 - Prob. 69ECh. 9.3 - Prob. 1YTCh. 9.3 - Prob. 2YTCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Find all points where the functions have any...Ch. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - Prob. 29ECh. 9.3 - Let f(x,y)=y22x2y+4x3+20x2. The only critical...Ch. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - Prob. 34ECh. 9.3 - Prob. 35ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.3 - Prob. 39ECh. 9.3 - Prob. 40ECh. 9.3 - Prob. 41ECh. 9.4 - Prob. 1YTCh. 9.4 - Prob. 2YTCh. 9.4 - Prob. 3YTCh. 9.4 - Evaluate dzusing the given information....Ch. 9.4 - Evaluate dzusing the given information....Ch. 9.4 - Evaluate dzusing the given the information....Ch. 9.4 - Evaluate dzusing the given information....Ch. 9.4 - Multivariable Calculus Total Differentials and...Ch. 9.4 - Evaluate dzusing the given information....Ch. 9.4 - Use the total differential to approximate each...Ch. 9.4 - Use the total differential to approximate each...Ch. 9.4 - Use the total differential to approximate each...Ch. 9.4 - Use the total differential to approximate each...Ch. 9.4 - Use the total differential to approximate each...Ch. 9.4 - Use the total differential to approximate each...Ch. 9.4 - Use the total differential to approximate each...Ch. 9.4 - Use the total differential to approximate each...Ch. 9.4 - Use the total differential to approximate each...Ch. 9.4 - Prob. 16ECh. 9.4 - Blood Vessel Volume A portion of a blood vessel is...Ch. 9.4 - Multivariable Calculus Total Differentials and...Ch. 9.4 - Multivariable Calculus Total Differentials and...Ch. 9.4 - Dialysis A model that estimates the concentration...Ch. 9.4 - Multivariable Calculus Total Differentials and...Ch. 9.4 - Eastern Hemlock Ring shake, which is the...Ch. 9.4 - Multivariable Calculus Total Differentials and...Ch. 9.4 - Multivariable Calculus Total Differentials and...Ch. 9.4 - Multivariable Calculus Total Differentials and...Ch. 9.4 - Prob. 29ECh. 9.4 - Prob. 30ECh. 9.4 - Multivariable Calculus Total Differentials and...Ch. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - Prob. 35ECh. 9.5 - Prob. 1YTCh. 9.5 - Prob. 2YTCh. 9.5 - Prob. 3YTCh. 9.5 - Prob. 4YTCh. 9.5 - Prob. 5YTCh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - EXERCISES Evaluate each integral. 15ye4x+y2dxCh. 9.5 - EXERCISES Evaluate each iterated integral. Many of...Ch. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - EXERCISES Find each double integral over the...Ch. 9.5 - EXERCISES Find each double integral over the...Ch. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - EXERCISES Find each double integral over the...Ch. 9.5 - Prob. 26ECh. 9.5 - EXERCISES Find each double integral over the...Ch. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - EXERCISES Find each double integral over the...Ch. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.5 - Prob. 36ECh. 9.5 - Prob. 37ECh. 9.5 - Prob. 38ECh. 9.5 - Prob. 39ECh. 9.5 - Prob. 40ECh. 9.5 - Prob. 41ECh. 9.5 - Prob. 42ECh. 9.5 - Prob. 43ECh. 9.5 - Prob. 44ECh. 9.5 - Prob. 45ECh. 9.5 - Prob. 46ECh. 9.5 - Prob. 47ECh. 9.5 - Prob. 48ECh. 9.5 - Prob. 49ECh. 9.5 - Prob. 50ECh. 9.5 - Prob. 51ECh. 9.5 - Prob. 52ECh. 9.5 - EXERCISES Use the region R with the indicated...Ch. 9.5 - EXERCISES Use the region R with the indicated...Ch. 9.5 - Prob. 55ECh. 9.5 - EXERCISES Use the region R with the indicated...Ch. 9.5 - Prob. 57ECh. 9.5 - Prob. 58ECh. 9.5 - Prob. 59ECh. 9.5 - Prob. 60ECh. 9.5 - Prob. 61ECh. 9.5 - Prob. 63ECh. 9.5 - Prob. 64ECh. 9.5 - Prob. 65ECh. 9.5 - Prob. 66ECh. 9.5 - Prob. 67ECh. 9.5 - Prob. 68ECh. 9.5 - Prob. 69ECh. 9.5 - Prob. 70ECh. 9.CR - Determine whether each of the following statements...Ch. 9.CR - Prob. 2CRCh. 9.CR - Prob. 3CRCh. 9.CR - Prob. 4CRCh. 9.CR - Prob. 5CRCh. 9.CR - Prob. 6CRCh. 9.CR - Prob. 7CRCh. 9.CR - Prob. 8CRCh. 9.CR - Prob. 9CRCh. 9.CR - Prob. 10CRCh. 9.CR - Prob. 11CRCh. 9.CR - Prob. 12CRCh. 9.CR - Prob. 13CRCh. 9.CR - Prob. 14CRCh. 9.CR - Prob. 15CRCh. 9.CR - Prob. 16CRCh. 9.CR - Prob. 17CRCh. 9.CR - Prob. 18CRCh. 9.CR - Prob. 19CRCh. 9.CR - Prob. 20CRCh. 9.CR - Prob. 21CRCh. 9.CR - Prob. 22CRCh. 9.CR - Prob. 23CRCh. 9.CR - Prob. 24CRCh. 9.CR - Prob. 25CRCh. 9.CR - Prob. 26CRCh. 9.CR - Prob. 27CRCh. 9.CR - Prob. 28CRCh. 9.CR - Prob. 29CRCh. 9.CR - Prob. 30CRCh. 9.CR - Prob. 31CRCh. 9.CR - Prob. 32CRCh. 9.CR - Prob. 33CRCh. 9.CR - Prob. 34CRCh. 9.CR - Prob. 35CRCh. 9.CR - Prob. 36CRCh. 9.CR - Prob. 37CRCh. 9.CR - Prob. 38CRCh. 9.CR - Prob. 39CRCh. 9.CR - Prob. 40CRCh. 9.CR - Prob. 41CRCh. 9.CR - Prob. 42CRCh. 9.CR - Prob. 43CRCh. 9.CR - Prob. 44CRCh. 9.CR - Prob. 45CRCh. 9.CR - Prob. 46CRCh. 9.CR - Prob. 47CRCh. 9.CR - Prob. 48CRCh. 9.CR - Prob. 49CRCh. 9.CR - Prob. 50CRCh. 9.CR - Prob. 51CRCh. 9.CR - Prob. 52CRCh. 9.CR - Prob. 53CRCh. 9.CR - Prob. 54CRCh. 9.CR - Prob. 55CRCh. 9.CR - Prob. 56CRCh. 9.CR - Prob. 57CRCh. 9.CR - Prob. 58CRCh. 9.CR - Prob. 59CRCh. 9.CR - Prob. 60CRCh. 9.CR - Prob. 61CRCh. 9.CR - Prob. 62CRCh. 9.CR - Prob. 63CRCh. 9.CR - Prob. 64CRCh. 9.CR - Prob. 65CRCh. 9.CR - Prob. 66CRCh. 9.CR - Prob. 67CRCh. 9.CR - Prob. 68CRCh. 9.CR - Prob. 69CRCh. 9.CR - Prob. 70CRCh. 9.CR - Prob. 71CRCh. 9.CR - Prob. 72CRCh. 9.CR - Prob. 73CRCh. 9.CR - Prob. 74CRCh. 9.CR - Prob. 75CRCh. 9.CR - Prob. 76CRCh. 9.CR - Prob. 77CRCh. 9.CR - Prob. 78CRCh. 9.CR - Prob. 79CRCh. 9.CR - Prob. 80CRCh. 9.CR - Prob. 81CRCh. 9.CR - Prob. 82CRCh. 9.CR - Prob. 83CRCh. 9.CR - Prob. 84CRCh. 9.CR - Prob. 85CRCh. 9.CR - Prob. 86CRCh. 9.CR - Prob. 88CRCh. 9.CR - Prob. 89CRCh. 9.CR - Prob. 90CRCh. 9.CR - Prob. 91CRCh. 9.CR - Prob. 92CRCh. 9.CR - Prob. 93CRCh. 9.CR - Prob. 94CRCh. 9.CR - Prob. 95CRCh. 9.CR - Prob. 96CRCh. 9.CR - Prob. 97CRCh. 9.CR - Production Error The height of a sample cone from...Ch. 9.CR - Prob. 99CRCh. 9.EA - Prob. 1EACh. 9.EA - Prob. 2EA
Knowledge Booster
Background pattern image
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Text book image
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
SEE MORE TEXTBOOKS
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY