In Exercises 1-4, decide whetlier ttie problem can be solved using precalculus, or whether calculus is required. If the prob- lem can be solved using precalculus, solve it. If the problem seems to require calculus, explain vour reasoning and use a graphical or numerical approach to estimate the solution. Find the distance traveled in 15 seconds hy an object traveling at a constant velocity of 20 feet per second
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Table of Contents
P
Preparation for Calculus
P.1
Graphs and Models
P.2
Linear Models and Rates of Change
P.3
Functions and Their Graph's
P.4
Fitting Models to Data
1
Limits and Their Properties
1.1
A Preview of Calculus
1.2
Finding Limits Graphically and Numerically
1.3
Evaluating Limits Analytically
1.4
Continuity and One-Sided Limits
1.5
Infinite Limits
2
Differentiation
2.1
The Derivative and the Tangent Line Problem
2.2
Basic Differentiation Rules and Rates of Change
2.3
The Product and Quotient Rules and Higher-Order Derivatives
2.4
The Chain Rule
2.5
Implicit Differentation
2.6
Related Rates
3
Applications of Differentation
3.1
Extrema on an Interval
3.2
Rolle's Theorem and the Mean Value Theorem
3.3
Increasmg and Decreasing Functions and the First Derivative Test
3.4
Concavity and the Second Derivative Test
3.5
Limits at Infinity
3.6
A Summary of Curve Sketching
3.7
Optimization Problems
3.8
Newton's Method
3.9
Differentials
4
Integration
4.1
Antiderivatives and Indefinite Integration
4.2
Area
4.3
Riemann Sums and Definite Integrals
4.4
The Fimdamental Theorem of Calculus
4.5
Integration by Substitution
4.6
Numerical Integration
5
Logaritliniic, Exponential, and Other TianscenUcntal Functions
5.1
The Natural Logarithmic Function: Differentiation
5.2
The Natural Logarithmic Function: Integration
5.3
Inverse Fimctions
5.4
Exponential Functions: Differentiation and Integration
5.5
Bases Other than e and Applications
5.6
Differential Equations: Growth and Decay
5.7
Differential Equations: Separation of Variables
5.8
Inverse Trigonometric Functions: Differentiation
5.9
Inverse Trigonometric Functions: Integration
6
Applications of Integration
6.1
Area of a Region Between Two Curves
6.2
Volume: The Disk Method
6.3
Volume: The Shell Method
6.4
Arc Lencth and Surfaces of Ro\nliition
6.5
Work
6.6
Monicnls. Centers of Mass, and Centioids
6.7
Fluid Pressure and Fluid Force
7
Integraticm Techniques, L^Hopital's Rule, and Improper Integrals
7.1
BLisic liilesjration Rules
7.2
lntegralion by Parts
7.3
Trigonometric Integrals
7.4
Trigonometric Substitution
7.5
Partial Fractions
7.6
Integration by Tables and Other Integration Techniques
7.7
Indeterminate Forms and l/Hopital's Rule
7.8
Improper Integrals
8
Infinite Series
8.1
Sequences
8.10
Tarjrior iwia Maclaurin Series
8.2
Series and Convergence
8.3
The Integral Test and Series
8.4
Comparisons of Series
8.5
Alternating Series
8.6
The Ratio and Root Tests
8.7
Taylor Polynomials and ApprOxiniatlons
8.8
Power Series
8.9
Representation of Functions by Power Series
9
Conies. Parametric Equations, and Polar Coordinates
9.1
Conics and Calculus
9.2
Plane Curves and Parametric Equations
9.3
Parametric Equations and Calculus
9.4
Polar Cqordmates and Polar Graphs
9.5
Area andArc Length in Polar Coordinates
9.6
Polar Equations of Conies and Kepler's Laws
Textbook Solutions for Calculus of A Single Variable
Chapter 1.1 Problem 9
Question
(a) Use the list feature of a graphing utility to graph the following. = 4.V - .V\V|(1 + 12. 1.5. 1.0.51) - V|(l) 1.5. 1.0.51 (.V- l) + v,(l) (b) (c) 10. la) (Note: If you cannot use lists on your graphing utMity, graph Vt four times using 2, 1.5. 1. and 0.5.) Give a written description of the graphs of v, relative to the graph of y,. Use the results in part (a) to estimate the slope of the tangent line to the graph of v, at ( I . .^), It you want to improve your approximation of the slope, how could you change the list in the formula for v,'.'
Solution
The first step in solving 1.1 problem number 9 trying to solve the problem we have to refer to the textbook question: (a) Use the list feature of a graphing utility to graph the following. = 4.V - .V\V|(1 + 12. 1.5. 1.0.51) - V|(l) 1.5. 1.0.51 (.V- l) + v,(l) (b) (c) 10. la) (Note: If you cannot use lists on your graphing utMity, graph Vt four times using 2, 1.5. 1. and 0.5.) Give a written description of the graphs of v, relative to the graph of y,. Use the results in part (a) to estimate the slope of the tangent line to the graph of v, at ( I . .^), It you want to improve your approximation of the slope, how could you change the list in the formula for v,'.'
From the textbook chapter A Preview of Calculus you will find a few key concepts needed to solve this.
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full solution
Title
Calculus of A Single Variable 7
Author
Ron Larson, Robert P. Hostetler, Bruce H. Edwards, David E. Heyd
ISBN
9780618149162
(a) Use the list feature of a graphing utility to graph the following. = 4.V - .V\V
Chapter 1.1 textbook questions
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Chapter 1: Problem 1 Calculus of A Single Variable 7
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Chapter 1: Problem 2 Calculus of A Single Variable 7
In Exercises 1-4, decide whetlier ttie problem can be solved using precalculus, or whether calculus is required. If the prob- lem can be solved using precalculus, solve it. If the problem seems to require calculus, explain vour reasoning and use a graphical or numerical approach to estimate the solution. Find the distance traveled in 15 seconds by an object moving with a velocity of r(r) = 20 + 7 cos i feet per second.
Read more -
Chapter 1: Problem 3 Calculus of A Single Variable 7
In Exercises 1-4, decide whetlier ttie problem can be solved using precalculus, or whether calculus is required. If the prob- lem can be solved using precalculus, solve it. If the problem seems to require calculus, explain vour reasoning and use a graphical or numerical approach to estimate the solution. A bicyclist is riding on a path modeled by the function fix) = 0.04(8.v - .v-^). where .v and /(.v) are measured in miles. Find the rate of chauizc of elevation when .v = 2.
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Chapter 1: Problem 4 Calculus of A Single Variable 7
In Exercises 1-4, decide whetlier ttie problem can be solved using precalculus, or whether calculus is required. If the prob- lem can be solved using precalculus, solve it. If the problem seems to require calculus, explain vour reasoning and use a graphical or numerical approach to estimate the solution. A bicvclist is riding on a path modeled by the function fix) = 0.()8.v, where v and/fv) are measured in miles. Find the rate of change of elevation when .v =
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Chapter 1: Problem 5 Calculus of A Single Variable 7
In Exercises 5 and 6, find the area of the shaded region.
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Chapter 1: Problem 6 Calculus of A Single Variable 7
In Exercises 5 and 6, find the area of the shaded region.
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Chapter 1: Problem 7 Calculus of A Single Variable 7
In Exercises 7 and 8, find the volume of the solid shown.
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Chapter 1: Problem 8 Calculus of A Single Variable 7
In Exercises 7 and 8, find the volume of the solid shown.
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Chapter 1: Problem 9 Calculus of A Single Variable 7
(a) Use the list feature of a graphing utility to graph the following. = 4.V - .V\V|(1 + 12. 1.5. 1.0.51) - V|(l) 1.5. 1.0.51 (.V- l) + v,(l) (b) (c) 10. la) (Note: If you cannot use lists on your graphing utMity, graph Vt four times using 2, 1.5. 1. and 0.5.) Give a written description of the graphs of v, relative to the graph of y,. Use the results in part (a) to estimate the slope of the tangent line to the graph of v, at ( I . .^), It you want to improve your approximation of the slope, how could you change the list in the formula for v,'.'
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Chapter 1: Problem 10 Calculus of A Single Variable 7
la) (Note: If you cannot use lists on your graphing utMity, graph Vt four times using 2, 1.5. 1. and 0.5.) Give a written description of the graphs of v, relative to the graph of y,. Use the results in part (a) to estimate the slope of the tangent line to the graph of v, at ( I . .^), It you want to improve your approximation of the slope, how could you change the list in the formula for v,'.' flse the rectangles in each graph to appro.\imate the area of the region hoiuided by v = 5/.v. y = 0, .v = I, and .V = 5 . 4 \\ 3+ \ 2 X. 1 "==^ 12 3 4 5 (b) Describe how you could continue this process to obtain a more accurate approximation of the area.
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Chapter 1: Problem 11 Calculus of A Single Variable 7
Consider the length of the graph of fix) = 5/.v from (1.5) to (5, I). 5- (1.5) 4- - y . 3 - 2 - 1- 1 1 2 3 4 5 (1.5) 5 - \ 4- 3- \ 1 ~ V I - \V- (5. 11 1 2 3 4 5 (a) .Approximate the length of the curve by finding the distance between its two endpoints. as shown in the first figure. (b) Approximate the length of the curve by finding the lengths of four line segments, as shown in the second figure. (c) Describe how you could continue this process to obtain a more accurate approximation of the length of the curve.
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