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Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759

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Section
BuyFindarrow_forward

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759
Chapter 2.1, Problem 50E
Textbook Problem
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Difference Quotient Find f(a), f(a + h), and the difference quotient, f ( a + h ) f ( a ) h , where h ≠ 0.

50. f(x) = x3

To determine

To evaluate: The values of f(a) , f(a+h) and f(a+h)f(a)h for the function f(x)=x3 .

Explanation of Solution

Given:

The given function is,

f(x)=x3 (1)

Calculation:

Substitute a for x in equation (1) to find the value of f(a) for the function f(x)=x3 ,

f(a)=(a)3=a3

Thus, the value of f(a) for the function f(x)=x3 is a3 .

Calculate the value of f(a+h) for the given function as follows.

Substitute (a+h) for x in equation (1), to find the value of f(a+h) for the function f(x)=x3 ,

f(a+h)=(a+h)3=a3+3a2h+3ah2+h3

Thus, the value of f(a+h) for the function f(x)=x3 is a3+3a2h+3ah2+h3 .

Calculate the value of f(a+h)f(a)h for the given function as follows

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Precalculus: Mathematics for Calculus (Standalone Book)
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From the graphs of f and g in the figure, we find...Ch. 2.7 - By definition, (f g)(x) = _____. So if g(2) = 5...Ch. 2.7 - If the rule of the function f is add one and the...Ch. 2.7 - We can express the functions in Exercise 3...Ch. 2.7 - Let f and g be functions. 5. (a) The function (f +...Ch. 2.7 - Let f and g be functions. 6. The composition (f ...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Combining Functions Find f + g, f g, fg, and f/g...Ch. 2.7 - Domain Find the domain of the function. 17....Ch. 2.7 - Domain Find the domain of the function. 18....Ch. 2.7 - Domain Find the domain of the function. 19. h(x) =...Ch. 2.7 - Domain Find the domain of the function. 20....Ch. 2.7 - Graphical Addition Use graphical addition to...Ch. 2.7 - Graphical Addition Use graphical addition to...Ch. 2.7 - Graphical Addition Draw the graphs of f, g, and f...Ch. 2.7 - Graphical Addition Draw the graphs of f, g, and f...Ch. 2.7 - Graphical Addition Draw the graphs of f, g, and f...Ch. 2.7 - Graphical Addition Draw the graphs of f, g, and f...Ch. 2.7 - Evaluating Composition of Functions Use f(x) = 2x ...Ch. 2.7 - Evaluating Composition of Functions Use f(x) = 2x ...Ch. 2.7 - Evaluating Composition of Functions Use f(x) = 2x ...Ch. 2.7 - Evaluating Composition of Functions Use f(x) = 2x ...Ch. 2.7 - Evaluating Composition of Functions Use f(x) = 2x ...Ch. 2.7 - Evaluating Composition of Functions Use f(x) = 2x ...Ch. 2.7 - Composition Using a Graph Use the given graphs of...Ch. 2.7 - Composition Using a Graph Use the given graphs of...Ch. 2.7 - Composition Using a Graph Use the given graphs of...Ch. 2.7 - Composition Using a Graph Use the given graphs of...Ch. 2.7 - Composition Using a Graph Use the given graphs of...Ch. 2.7 - Composition Using a Graph Use the given graphs of...Ch. 2.7 - Composition Using a Table Use the table to...Ch. 2.7 - Composition Using a Table Use the table to...Ch. 2.7 - Composition Using a Table Use the table to...Ch. 2.7 - Composition Using a Table Use the table to...Ch. 2.7 - Composition Using a Table Use the table to...Ch. 2.7 - Composition Using a Table Use the table to...Ch. 2.7 - Composition Using a Table Use the table to...Ch. 2.7 - Composition Using a Table Use the table to...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Functions Find the functions f g,...Ch. 2.7 - Composition of Three Functions Find f g h. 59....Ch. 2.7 - Composition of Three Functions Find f g h. 60....Ch. 2.7 - Composition of Three Functions Find f g h. 61....Ch. 2.7 - Composition of Three Functions Find f g h. 62....Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Expressing a Function as a Composition Express the...Ch. 2.7 - Composing Linear Functions The graphs of the...Ch. 2.7 - Solving an Equation for an Unknown Function...Ch. 2.7 - Revenue, Cost, and Profit A print shop makes...Ch. 2.7 - Revenue, Cost, and Profit A print shop makes...Ch. 2.7 - Area of a Ripple A stone is dropped in a lake,...Ch. 2.7 - Inflating a Balloon A spherical balloon is being...Ch. 2.7 - Area of a Balloon A spherical weather balloon is...Ch. 2.7 - Multiple Discounts You have a 50 coupon from the...Ch. 2.7 - Multiple Discounts An appliance dealer advertises...Ch. 2.7 - Airplane Trajectory An airplane is flying at a...Ch. 2.7 - DISCOVER: Compound Interest A savings account...Ch. 2.7 - DISCUSS: Compositions of Odd and Even Functions...Ch. 2.8 - A function f is one-to-one if different inputs...Ch. 2.8 - (a) For a function to have an inverse, it must be...Ch. 2.8 - A function f has the following verbal description:...Ch. 2.8 - A graph of a function f is given. Does f have an...Ch. 2.8 - If the point (3, 4) is on the graph of the...Ch. 2.8 - True or false? (a) If f has an inverse, then f1(x)...Ch. 2.8 - One-to-One Function? A graph of a function f is...Ch. 2.8 - One-to-One Function? A graph of a function f is...Ch. 2.8 - One-to-One Function? A graph of a function f is...Ch. 2.8 - One-to-One Function? A graph of a function f is...Ch. 2.8 - One-to-One Function? A graph of a function f is...Ch. 2.8 - One-to-One Function? A graph of a function f is...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - One-to-One Function? Determine whether the...Ch. 2.8 - Finding Values of an Inverse Function Assume that...Ch. 2.8 - Finding Values of an Inverse Function Assume that...Ch. 2.8 - Finding Values of an Inverse Function Assume that...Ch. 2.8 - Finding Values of an Inverse Function Assume that...Ch. 2.8 - Finding Values of an Inverse from a Graph A graph...Ch. 2.8 - Finding Values of an Inverse from a Graph A graph...Ch. 2.8 - Finding Values of an Inverse Using a Table A table...Ch. 2.8 - Finding Values of an Inverse Using a Table A table...Ch. 2.8 - Finding Values of an Inverse Using a Table A table...Ch. 2.8 - Finding Values of an Inverse Using a Table A table...Ch. 2.8 - Finding Values of an Inverse Using a Table A table...Ch. 2.8 - Finding Values of an Inverse Using a Table A table...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Inverse Function Property Use the Inverse Function...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Finding Inverse Functions Find the inverse...Ch. 2.8 - Graph of an Inverse Function A function f is...Ch. 2.8 - Graph of an Inverse Function A function f is...Ch. 2.8 - Graph of an Inverse Function A function f is...Ch. 2.8 - Graph of an Inverse Function A function f is...Ch. 2.8 - One-to-One Functions from a Graph Draw the graph...Ch. 2.8 - One-to-One Functions from a Graph Draw the graph...Ch. 2.8 - One-to-One Functions from a Graph Draw the graph...Ch. 2.8 - One-to-One Functions from a Graph Draw the graph...Ch. 2.8 - One-to-One Functions from a Graph Draw the graph...Ch. 2.8 - One-to-One Functions from a Graph Draw the graph...Ch. 2.8 - Finding Inverse Functions A one-to-one function is...Ch. 2.8 - Finding Inverse Functions A one-to-one function is...Ch. 2.8 - Finding Inverse Functions A one-to-one function is...Ch. 2.8 - Finding Inverse Functions A one-to-one function is...Ch. 2.8 - Restricting the Domain The given function is not...Ch. 2.8 - Restricting the Domain The given function is not...Ch. 2.8 - Restricting the Domain The given function is not...Ch. 2.8 - Restricting the Domain The given function is not...Ch. 2.8 - Graph of an Inverse Function Use the graph of f to...Ch. 2.8 - Graph of an Inverse Function Use the graph of f to...Ch. 2.8 - Functions That Are Their Own Inverse If a function...Ch. 2.8 - Functions That Are Their Own Inverse If a function...Ch. 2.8 - Pizza Cost Marcellos Pizza charges a base price of...Ch. 2.8 - Fee for Service For his services, a private...Ch. 2.8 - Torricellis Law A tank holds 100 gallons of water,...Ch. 2.8 - Blood Flow As blood moves through a vein or...Ch. 2.8 - Demand Function The amount of a commodity that is...Ch. 2.8 - Temperature Scales The relationship between the...Ch. 2.8 - Exchange Rates The relative value of currencies...Ch. 2.8 - Income Tax In a certain country the tax on incomes...Ch. 2.8 - Multiple Discounts A car dealership advertises a...Ch. 2.8 - DISCUSS: Determining When a Linear Function Has an...Ch. 2.8 - DISCUSS: Finding an Inverse In Your Head In the...Ch. 2.8 - PROVE: The Identity Function The function I(x) = x...Ch. 2.8 - DISCUSS: Solving an Equation for an Unknown...Ch. 2 - Define each concept. (a) Function (b) Domain and...Ch. 2 - Describe the four ways of representing a function.Ch. 2 - Sketch graphs of the following functions by hand....Ch. 2 - What is a piecewise defined function? Give an...Ch. 2 - (a) What is the Vertical Line Test, and what is it...Ch. 2 - Define each concept, and give an example of each....Ch. 2 - Suppose we know that the point (3, 5) is a point...Ch. 2 - What does it mean to say that f(4) is a local...Ch. 2 - Explain how to find the average rate of change of...Ch. 2 - (a) What is the slope of a linear function? How do...Ch. 2 - Suppose the graph of a function f is given. Write...Ch. 2 - (a) What is an even function? How can you tell...Ch. 2 - Suppose that f has domain A and g has domain B....Ch. 2 - (a) How is the composition function f g defined?...Ch. 2 - (a) What is a one-to-one function? (b) How can you...Ch. 2 - Function Notation A verbal description of a...Ch. 2 - Function Notation A verbal description of a...Ch. 2 - Function in Words A formula for a function f is...Ch. 2 - Function in Words A formula for a function f is...Ch. 2 - Table of Values Complete the table of values for...Ch. 2 - Table of Values Complete the table of values for...Ch. 2 - Printing Cost A publisher estimates that the cost...Ch. 2 - Earnings Reynalda works as a salesperson in the...Ch. 2 - Evaluating Functions Evaluate the function at the...Ch. 2 - Evaluating Functions Evaluate the function at the...Ch. 2 - Functions Given by a Graph Which of the following...Ch. 2 - Getting Information from a Graph A graph of a...Ch. 2 - Domain and Range Find the domain and range of the...Ch. 2 - Domain and Range Find the domain and range of the...Ch. 2 - Domain Find the domain of the function. 15. f(x) =...Ch. 2 - Domain Find the domain of the function. 16....Ch. 2 - Domain Find the domain of the function. 17....Ch. 2 - Domain Find the domain of the function. 18....Ch. 2 - Domain Find the domain of the function. 19....Ch. 2 - Domain Find the domain of the function. 20....Ch. 2 - Domain Find the domain of the function. 21....Ch. 2 - Domain Find the domain of the function. 22....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Graphing Functions Sketch a graph of the function....Ch. 2 - Equations That Represent Functions Determine...Ch. 2 - Equations That Represent Functions Determine...Ch. 2 - Equations That Represent Functions Determine...Ch. 2 - Equations That Represent Functions Determine...Ch. 2 - Graphing Functions Determine which viewing...Ch. 2 - Graphing Functions Determine which viewing...Ch. 2 - Domain and Range from a Graph A function f is...Ch. 2 - Domain and Range from a Graph A function f is...Ch. 2 - Domain and Range from a Graph A function f is...Ch. 2 - Domain and Range from a Graph A function f is...Ch. 2 - Getting Information from a Graph Draw a graph of...Ch. 2 - Getting Information from a Graph Draw a graph of...Ch. 2 - Net Change and Average Rate of Change A function...Ch. 2 - Net Change and Average Rate of Change A function...Ch. 2 - Net Change and Average Rate of Change A function...Ch. 2 - Net Change and Average Rate of Change A function...Ch. 2 - Net Change and Average Rate of Change A function...Ch. 2 - Net Change and Average Rate of Change A function...Ch. 2 - Linear? Determine whether the given function is...Ch. 2 - Linear? Determine whether the given function is...Ch. 2 - Linear Functions A linear function is given. (a)...Ch. 2 - Linear Functions A linear function is given. (a)...Ch. 2 - Linear Functions A linear function is described...Ch. 2 - Linear Functions A linear function is described...Ch. 2 - Linear Functions A linear function is described...Ch. 2 - Linear Functions A linear function is described...Ch. 2 - Linear Functions A linear function is described...Ch. 2 - Linear Functions A linear function is described...Ch. 2 - Population The population of a planned seaside...Ch. 2 - Retirement Savings Ella is saving for her...Ch. 2 - Average Rate of Change A function f is given. (a)...Ch. 2 - Average Rate of Change A function f is given. (a)...Ch. 2 - Transformations Suppose the graph of f is given....Ch. 2 - Transformations The graph of f is given. Draw the...Ch. 2 - Even and Odd Functions Determine whether f is...Ch. 2 - Even and Odd Functions Determine whether the...Ch. 2 - Local Maxima and Minima Find the local maximum and...Ch. 2 - Local Maxima and Minima Find the local maximum and...Ch. 2 - Local Maxima and Minima Find the local maximum and...Ch. 2 - Local Maxima and Minima Find the local maximum and...Ch. 2 - Maximum Height of Projectile A stone is thrown...Ch. 2 - Maximum Profit The profit P (in dollars) generated...Ch. 2 - Graphical Addition Two functions, f and g, are...Ch. 2 - Graphical Addition Two functions, f and g, are...Ch. 2 - Combining Functions If f(x) = x2 3x + 2 and g(x)...Ch. 2 - If f(x) = 1 + x2 and g(x)=x1, find the following....Ch. 2 - Composition of Functions Find the functions f g,...Ch. 2 - Composition of Functions Find the functions f g,...Ch. 2 - Finding a Composition Find f g h, where...Ch. 2 - Finding a Composition If T(x)1+x, find functions...Ch. 2 - One-to-One Functions Determine whether the...Ch. 2 - g(x) = 2 2x+ x2Ch. 2 - One-to-One Functions Determine whether the...Ch. 2 - One-to-One Functions Determine whether the...Ch. 2 - One-to-One Functions Determine whether the...Ch. 2 - One-to-One Functions Determine whether the...Ch. 2 - Finding Inverse Functions Find the inverse of the...Ch. 2 - Finding Inverse Functions Find the inverse of the...Ch. 2 - Finding Inverse Functions Find the inverse of the...Ch. 2 - Finding Inverse Functions Find the inverse of the...Ch. 2 - Inverse Functions from a Graph A graph of a...Ch. 2 - Inverse Functions from a Graph A graph of a...Ch. 2 - Graphing Inverse Functions (a) Sketch a graph of...Ch. 2 - Graphing Inverse Functions (a) Show that the...Ch. 2 - Which of the following are graphs of functions? If...Ch. 2 - Let f(x)=xx+1. (a) Evaluate f(0), f(2), and f(a +...Ch. 2 - A function f has the following verbal description:...Ch. 2 - A graph of a function f is given in the margin....Ch. 2 - A school fund-raising group sells chocolate bars...Ch. 2 - Determine the net change and the average rate of...Ch. 2 - Let f(x) = (x + 5)2 and g(x) = 1 5x. (a) Only one...Ch. 2 - (a) Sketch the graph of the function f(x) = x3....Ch. 2 - (a) How is the graph of y = f(x 3) + 2 obtained...Ch. 2 - Let f(x)={1xifx12x+1ifx1 (a) Evaluate f(2) and...Ch. 2 - If f(x) = x2 + x + 1 and g(x) = x 3, find the...Ch. 2 - Determine whether the function is one-to-one. (a)...Ch. 2 - Use the Inverse Function Property to show that...Ch. 2 - Find the inverse function of f(x)=x32x+5.Ch. 2 - (a) If f(x)=3x, find the inverse function f1. (b)...Ch. 2 - A graph of a function f is given below. 16. Find...Ch. 2 - A graph of a function f is given below. 17. Find...Ch. 2 - A graph of a function f is given below. 18. Graph...Ch. 2 - A graph of a function f is given below. 19. Find...Ch. 2 - A graph of a function f is given below. 20. Find...Ch. 2 - A graph of a function f is given below. 21. Sketch...Ch. 2 - Let f(x) = 3x4 14x2 + 5x 3. (a) Draw the graph...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - In these problems you are asked to find a function...Ch. 2 - Length A woman 5 ft tall is standing near a street...Ch. 2 - Distance Two ships leave port at the same time....Ch. 2 - Product The sum of two positive numbers is 60....Ch. 2 - Area An isosceles triangle has a perimeter of 8...Ch. 2 - Perimeter A right triangle has one leg twice as...Ch. 2 - Area A rectangle is inscribed in a semicircle of...Ch. 2 - Height The volume of a cone is 100 in3. Find a...Ch. 2 - Maximizing a Product Consider the following...Ch. 2 - Minimizing a Sum Find two positive numbers whose...Ch. 2 - Fencing a Field Consider the following problem: A...Ch. 2 - Dividing a Pen A rancher with 750 ft of fencing...Ch. 2 - Fencing a Garden Plot A property owner wants to...Ch. 2 - Maximizing Area A wire 10 cm long is cut into two...Ch. 2 - Light from a Window A Norman window has the shape...Ch. 2 - Volume of a Box A box with an open top is to be...Ch. 2 - Area of a Box An open box with a square base is to...Ch. 2 - Inscribed Rectangle Find the dimensions that give...Ch. 2 - Minimizing Costs A rancher wants to build a...Ch. 2 - Minimizing Time A man stands at a point A on the...Ch. 2 - Bird Flight A bird is released from point A on an...Ch. 2 - Area of a Kite A kite frame is to be made from six...

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