Calculus For The Life Sciences 2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
P Prerequisite Skills Diagnostic Test R Algebra Reference 1 Functions 2 Exponential, Logarithmic, And Trigonometric Functions 3 The Derivative 4 Calculating The Derivative 5 Graphs And The Derivative 6 Applications Of The Derivative 7 Integration 8 Further Techniques And Applications Of Integration 9 Multivariable Calculus 10 Matrices 11 Differential Equations 12 Probability 13 Probability And Calculus 14 Discrete Dynamical Systems Chapter4: Calculating The Derivative
4.1 Techniques For Finding Derivatives 4.2 Derivatives Of Products And Quotients 4.3 The Chain Rule 4.4 Derivatives Of Exponential Functions 4.5 Derivatives Of Logarithmic Functions 4.6 Derivatives Of Trigonometric Functions 4.CR Chapter 4 Review 4.EA Extended Application Managing Renewable Resources Section4.3: The Chain Rule
Problem 1YT: YOUR TURN For the functions in Example 1, find fg0 and gf0. EXAMPLE 1 Composite functions Let... Problem 2YT: YOUR TURN Let fx=2x-3 and gx=x2+1. Find gfx. Problem 3YT: YOUR TURN Write hx=2x-33 as a composition of two functions f and g so that hx=fgx. Problem 4YT: YOUR TURN Find dy/dx if y=5x2-6x-2. Problem 5YT Problem 6YT Problem 7YT Problem 1E Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E Problem 7E Problem 8E Problem 9E Problem 10E Problem 11E: In Exercises 7-14, find f[gx] and g[fx]. fx=x+2; gx=8x2-6 Problem 12E: In Exercises 7-14, find f[gx] and g[fx]. fx=9x2-11x; gx=2x+2 Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E: Write each function as the composition of two functions. There may be more than more than one way to... Problem 21E Problem 22E: Find the derivative of each function defined as follows. y=2x3+9x5 Problem 23E Problem 24E: Find the derivative of each function defined as follows. fx=-73x4+2-4 Problem 25E Problem 26E Problem 27E: Find the derivative of each function defined as follows. gt=-37t3-1 Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E: Find the derivative of each function defined as follows. qy=4y2y2+15/4 Problem 34E: Find the derivative of each function defined as follows. pz=z6z+14/3 Problem 35E Problem 36E Problem 37E Problem 38E: Find the derivative of each function defined as follows. pt=2t+334t2-1 Problem 39E: Find the derivative of each function defined as follows. y=3x2-x2x-15 Problem 40E: Find the derivative of each function defined as follows. y=x2+4x3x3+24 Problem 41E Problem 42E Problem 43E Problem 44E: Consider the following table of values of the functions f and g and their derivatives at various... Problem 45E Problem 46E: In Exercises 45-48, find the equation of the tangent line to the graph of the given function at the... Problem 47E: In Exercises 45-48, find the equation of the tangent line to the graph of the given function at the... Problem 48E: In Exercises 45-48, find the equation of the tangent line to the graph of the given function at the... Problem 49E Problem 50E Problem 51E: Katie and Sarah are working on taking the derivative of fx=2x3x+4. Margy uses the quotient rule and... Problem 52E: Margy and Nate are working on taking the derivative of fx=23x+14. Margy uses the quotient rule and... Problem 53E Problem 54E: Oil Pollution An oil well off the Gulf Coast is leaking, with the leak spreading oil over the... Problem 55E: African Wild Dog The African wild dog is currently one of the most endangered carnivores in the... Problem 56E: Thermal Inversion When there is a thermal inversion layer over a city as happens often in Los... Problem 57E Problem 58E: Calcium Usage To test an individuals use of calcium, a researcher injects a small amount of... Problem 59E: Drug Reaction The strength of a persons reaction to a certain drug is given by RQ=QC-Q312, Where Q... Problem 61E: Extinction The probability of a population going extinct by time t when the birth and death rates... Problem 62E: Candy The volume and surface area of a jawbreaker for any radius is given by the formulas Vr=43r3... Problem 63E Problem 64E Problem 65E Problem 66E Problem 4YT: YOUR TURN Find dy/dx if y=5x2-6x-2.
4. Evaluate the triple integrals in Problems
Transcribed Image Text: 4.
L² L' S² (x² + 5y² – 2z) dr dy dz
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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