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 Section4.1: Techniques For Finding Derivatives
Problem 1YT: YOUR TURN If ft=1t, find f't. Problem 2YT Problem 3YT: YOUR TURN If ht=-3t2+2t+5t4-7, find h't. Problem 1E: Find the derivative of each function defined as follows. y=12x3-8x2+7x+5 Problem 2E: Find the derivative of each function defined as follows. y=8x3-5x2-x12 Problem 3E: Find the derivative of each function defined as follows. y=3x4-6x3+x28+5 Problem 4E: Find the derivative of each function defined as follows. y=5x4+9x3+12x2-7x Problem 5E: Find the derivative of each function defined as follows. fx=6x3.5-10x0.5 Problem 6E: Find the derivative of each function defined as follows. fx=-2x1.5+12x0.5 Problem 7E: Find the derivative of each function defined as follows. y=8x+6x3/4 Problem 8E: Find the derivative of each function defined as follows. y=-100x-11x2/3 Problem 9E: Find the derivative of each function defined as follows. y=10x-3+5x-4-8x Problem 10E: Find the derivative of each function defined as follows. y=5x-5-6x-2+13x-1 Problem 11E: Find the derivative of each function defined as follows. ft=7t-5t3 Problem 12E: Find the derivative of each function defined as follows. ft=14t+12t4+2 Problem 13E: Find the derivative of each function defined as follows. y=6x4-7x3+3x+5 Problem 14E: Find the derivative of each function defined as follows. y=3x6+1x5-7x2 Problem 15E: Find the derivative of each function defined as follows. px=-10x-1/2+8x-3/2 Problem 16E: Find the derivative of each function defined as follows. hx=x-1/2-14x-3/2 Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E: Which of the following describes the derivative function f'x of a quadratic function fx? a.... Problem 24E: Which of the following describes the derivative function f'x of a cubic third-degree function fx? a.... Problem 25E: Explain the relationship between the slope and the derivative of fx at x=a. Problem 26E Problem 27E: Find each derivative. Dx9x-1/2+2x3/2 Problem 28E: Find each derivative. Dx8x4-3x3 Problem 29E Problem 30E: Find each derivative. f'3 if fx=x39-7x2 Problem 31E: In Exercises 31-34, find the slope of the tangent line to the graph of the given equation at the... Problem 32E: In Exercises 31-34, find the slope of the tangent line to the graph of the given equation at the... Problem 33E: In Exercises 31-34, find the slope of the tangent line to the graph of the given equation at the... Problem 34E: In Exercises 31-34, find the slope of the tangent line to the graph of the given equation at the... Problem 35E Problem 36E: Find all points on the graph of fx=x3+9x2+19x-10 where the slope of the tangent line is -5. Problem 37E Problem 38E: In Exercises 37-40, for each function find all values of x where the tangent line is horizontal.... Problem 39E Problem 40E Problem 41E Problem 42E: At what point on the graph of fx=-5x2+4x-2 is the slope of the tangent line 6? Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E: In Exercises 43-46 of section 1.4, the effect of a when graphing y=af(x) was discussed. Now describe... Problem 49E: Show that, for any constant k, ddxfxk=f'xk. Problem 50E Problem 51E: Cancer Insulation workers who were exposed to asbestos and employed before 1960 experienced an... Problem 52E Problem 53E: Insect Mating Patterns In an experiment testing methods of sexually attracting male insects to... Problem 54E Problem 55E: Bighorn Sheep The cumulative horn volume for certain types of bighorn rams, found in the Rocky... Problem 56E: Brain Mass The brain mass of a human fetus during the last trimester can be accurately estimated... Problem 57E Problem 58E: Body Mass Index The body mass index BMI is a number that can be calculated for any inidividual as... Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E: Dogs Human Age From the data printed in the following table from the Minneapolis Star Tribune on... Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E: Postal Rates U.S postal rates have steadily increased since 1932. Using data depicted in the table... Problem 74E: Money The total amount of money in circulation for the years 1990-2012 can be closely approximated... Problem 75E Problem 35E
4.1.12 Intro To Real Analysis
Transcribed Image Text: 12. Show that the following limits do not exist.
1
(a)
lim
x→0x2
(x > 0),
(c) lim (x + sgn(x)),
x-0
(b)
lim
(x > 0),
x->0 √x
(d)
lim sin (1/x2).
x-0
Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
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