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Calculus

10th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781285057095
Chapter 3.6, Problem 5E
Textbook Problem
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Analyzing the Graph of a Function In Exercises 9-36, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.

y = 1 x 2 3

To determine

To graph: The function y=1x23

Explanation of Solution

Given: The function y=1x23.

Graph:

The function being a polynomial has a domain as all the real numbers except for 2.

The function can’t take the value -3 and thus the range of the function would be (,3)(3,).

Now by equating f(x) and x to zero respectively we will find the x and y intercepts

The x-intercept is (73,0) and the y-intercept is (0,72).

Now the function does have a vertical asymptote as x=2 because the denominator is not defined at 2.

Also,

limx(1x23)=limx(1x2)3=limx1x12x3=0103=3

This implies that the function has a horizontal asymptote as y=3

Now, differentiate the function with respect to x and equate it to zero to obtain the critical points.

1(x2)2=0

Clearly, this can never be zero and is not defined at 2 where the function is not defined itself. Hence, there are no critical points

This gives two test intervals (,2),(2,).

Let 0(,2).

f'(0)=1(02)2=14<0

The function is decreasing in this interval.

Let 3(2,).

f'(3)=1(32)2=1<0

The function is decreasing in this interval

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Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Finding Horizontal Asymptotes Using Technology In...Ch. 3.5 - Finding Horizontal Asymptotes Using Technology In...Ch. 3.5 - Finding Horizontal Asymptotes Using Technology In...Ch. 3.5 - Finding Horizontal Asymptotes Using Technology In...Ch. 3.5 - Finding a Limit In Exercises 41 and 42, find the...Ch. 3.5 - Finding a Limit In Exercises 41 and 42, find the...Ch. 3.5 - Finding a Limit In Exercises 43-46, find the...Ch. 3.5 - Finding a Limit In Exercises 43-46, find the...Ch. 3.5 - Finding a Limit In Exercises 43-46, find the...Ch. 3.5 - Finding a Limit In Exercises 43-46, find the...Ch. 3.5 - Numerical, Graphical, and Analytic Analysis In...Ch. 3.5 - Numerical, Graphical, and Analytic Analysis In...Ch. 3.5 - 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Sketching a Graph In Exercises 5974, sketch the...Ch. 3.5 - Sketching a Graph In Exercises 5974, sketch the...Ch. 3.5 - Sketching a Graph In Exercises 5974, sketch the...Ch. 3.5 - Sketching a Graph In Exercises 5974, sketch the...Ch. 3.5 - Sketching a Graph In Exercises 5974, sketch the...Ch. 3.5 - Sketching a Graph In Exercises 5974, sketch the...Ch. 3.5 - Sketching a Graph In Exercises 5974, sketch the...Ch. 3.5 - Analyzing a Graph Using Technology In Exercises...Ch. 3.5 - Analyzing a Graph Using Technology In Exercises...Ch. 3.5 - Analyzing a Graph Using Technology In Exercises...Ch. 3.5 - Analyzing a Graph Using Technology In Exercises...Ch. 3.5 - Analyzing a Graph Using Technology In Exercises...Ch. 3.5 - Analyzing a Graph Using Technology In Exercises...Ch. 3.5 - Analyzing a Graph Using Technology In Exercises...Ch. 3.5 - Analyzing a Graph Using Technology In Exercises...Ch. 3.5 - Comparing Functions In Exercises 83 and 84, (a)...Ch. 3.5 - Comparing Functions In Exercises 83 and 84, (a)...Ch. 3.5 - Engine Efficiency The efficiency (in percent) of...Ch. 3.5 - 86. Average Cost A business has a cost of C = 0.5x...Ch. 3.5 - Physics Newtons First Law of Motion and Einsteins...Ch. 3.5 - HOW DO YOU SEE IT? The graph shows the temperature...Ch. 3.5 - Modeling Data The average typing speeds S (in...Ch. 3.5 - Modeling Data A heat probe is attached to the heat...Ch. 3.5 - Using the Definition of Limits at Infinity The...Ch. 3.5 - Using the Definition of Limits at Infinity The...Ch. 3.5 - Using the Definition of Limits at Infinity...Ch. 3.5 - Using the Definition of Limits at Infinity...Ch. 3.5 - Proof In Exercises 63-66, use the definition of...Ch. 3.5 - Proof In Exercises 63-66, use the definition of...Ch. 3.5 - Proof In Exercises 6366, use the definition of...Ch. 3.5 - Proof In Exercises 6366, use the definition of...Ch. 3.5 - Distance A line with slope m passes through the...Ch. 3.5 - Distance A line with slope m passes through the...Ch. 3.5 - Proof Prove that if p(x) = anxn + + a1x + a0 and...Ch. 3.5 - Proof Use the definition of infinite limits at...Ch. 3.5 - True or False? In Exercises 103 and 104, determine...Ch. 3.5 - True or False? In Exercises 103 and 104, determine...Ch. 3.6 - Matching In Exercises 14, match the graph of f in...Ch. 3.6 - Matching In Exercises 14, match the graph of f in...Ch. 3.6 - Matching In Exercises 14, match the graph of f in...Ch. 3.6 - Matching In Exercises 14, match the graph of f in...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function InExercises...Ch. 3.6 - Analyzing the Graph of a Function InExercises...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - WRITING ABOUT CONCEPTS Using a Derivative Let...Ch. 3.6 - Using a Derivative Let f(0) = 3 and 2 f'(x) 4...Ch. 3.6 - Identifying Graphs In Exercises 51 and 52, the...Ch. 3.6 - Identifying Graphs In Exercises 51 and 52, the...Ch. 3.6 - Horizontal and Vertical Asymptotes In Exercises...Ch. 3.6 - Horizontal and Vertical Asymptotes In Exercises...Ch. 3.6 - Horizontal and Vertical Asymptotes In Exercises...Ch. 3.6 - Horizontal and Vertical Asymptotes In Exercises...Ch. 3.6 - Examining a Function In Exercises 69 and 70, use a...Ch. 3.6 - Examining a Function In Exercises 69 and 70, use a...Ch. 3.6 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Graphical Reasoning In Exercises 5356, use the...Ch. 3.6 - Graphical Reasoning In Exercises 5356, use the...Ch. 3.6 - Graphical Reasoning In Exercises 5356, use the...Ch. 3.6 - Graphical Reasoning In Exercises 5356, use the...Ch. 3.6 - Graphical Reasoning Consider the function...Ch. 3.6 - Graphical Reasoning Consider the function f(x) =...Ch. 3.6 - Graphical Reasoning Identify the real numbers...Ch. 3.6 - HOW DO YOU SEE IT? The graph of f is shown in the...Ch. 3.6 - Investigation Let P(x0,y0) be an arbitrary point...Ch. 3.6 - Investigation Consider the function f(x)=2xnx4+1...Ch. 3.6 - Graphical Reasoning Consider the function...Ch. 3.6 - Graphical Reasoning Consider the function...Ch. 3.6 - Slant Asymptotes In Exercises 91 and 92, the graph...Ch. 3.6 - Slant Asymptotes In Exercises 91 and 92, the graph...Ch. 3.6 - PUTNAM EXAM CHALLENGE Let f(x) be defined for axb....Ch. 3.6 - Think About It In Exercises 7982, create a...Ch. 3.6 - Think About It In Exercises 7982, create a...Ch. 3.6 - Think About It In Exercises 7982, create a...Ch. 3.6 - Think About It In Exercises 7982, create a...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis Find...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis An...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Finding Numbers In Exercises 38, find two positive...Ch. 3.7 - Finding Numbers In Exercises 5–10, find two...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Maximum Area In Exercises 11 and 12, find the...Ch. 3.7 - Maximum Area In Exercises 11 and 12, find the...Ch. 3.7 - Minimum Perimeter In Exercises 11 and 12, find the...Ch. 3.7 - Minimum Perimeter In Exercises 13 and 14, find the...Ch. 3.7 - Minimum Distance In Exercises 1316, find the point...Ch. 3.7 - Minimum Distance In Exercises 1316, find the point...Ch. 3.7 - Minimum Distance In Exercises 1316, find the point...Ch. 3.7 - Minimum Distance In Exercises 1316, find the point...Ch. 3.7 - Minimum Area A rectangular page is to contain 30...Ch. 3.7 - Minimum Area A rectangular page is to contain 36...Ch. 3.7 - Minimum Length A farmer plans to fence a...Ch. 3.7 - Maximum Volume A rectangular solid (with a square...Ch. 3.7 - Maximum Area A Norman window is constructed by...Ch. 3.7 - Maximum Area A rectangle is bounded by the x- and...Ch. 3.7 - Minimum Length and Minimum Area A right triangle...Ch. 3.7 - Maximum Area Find the area of the largest...Ch. 3.7 - Maximum Area A rectangle is bounded by the x-axis...Ch. 3.7 - Maximum Area Find the dimensions of the largest...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis An...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis A...Ch. 3.7 - Maximum Volume A rectangular package to be sent by...Ch. 3.7 - Maximum Volume Rework Exercise 29 for a...Ch. 3.7 - EXPLORING CONCEPTS Surface Area and Volume A...Ch. 3.7 - EXPLORING CONCEPTS Area and Perimeter The...Ch. 3.7 - Minimum Surface Area A solid is formed by...Ch. 3.7 - Minimum Cost An industrial tank of the shape...Ch. 3.7 - Minimum Area The sum of the perimeters of an...Ch. 3.7 - Maximum Area Twenty feet of wire is to be used to...Ch. 3.7 - Beam Strength A wooden beam has a rectangular...Ch. 3.7 - Minimum Length Two factories are located at the...Ch. 3.7 - Minimum Cost An offshore oil well is 2 kilometers...Ch. 3.7 - Illumination A light source is located over the...Ch. 3.7 - Minimum Time A man is in a boat 2 miles from the...Ch. 3.7 - Minimum Time The conditions are the same as in...Ch. 3.7 - Minimum Distance Sketch the graph of f(x)=22sinx...Ch. 3.7 - Minimum Time When light waves traveling in a...Ch. 3.7 - Maximum Volume A sector with central angle is cut...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis The...Ch. 3.7 - Maximum Profit Assume that the amount of money...Ch. 3.7 - HOW DO YOU SEE IT? The graph shows the profit P...Ch. 3.7 - Minimum Distance In Exercises 49-51, consider a...Ch. 3.7 - Minimum Distance In Exercises 49-51, consider a...Ch. 3.7 - Minimum Distance In Exercises 49-51, consider a...Ch. 3.7 - Maximum Area Consider a symmetric cross inscribed...Ch. 3.7 - PUTNAM EXAM CHALLENGE Find, with explanation, the...Ch. 3.7 - PUTNAM EXAM CHALLENGE Find the minimum value of...Ch. 3.8 - Using Newton's Method In Exercises 14, complete...Ch. 3.8 - Using Newton's Method In Exercises 3-6, calculate...Ch. 3.8 - Using Newtons Method In Exercises 3-6, calculate...Ch. 3.8 - Using Newtons Method In Exercises 3-6, calculate...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Using Newton's Method Consider the function...Ch. 3.8 - Using Newton's Method Repeat the steps in Exercise...Ch. 3.8 - Failure of Newton's Method In Exercises 23 and 24,...Ch. 3.8 - Failure of Newton's Method In Exercises 23 and 24,...Ch. 3.8 - Fixed Point In Exercises 25-26, approximate the...Ch. 3.8 - Fixed Point In Exercises 25 and 26, approximate...Ch. 3.8 - Approximating Reciprocals Use Newtons Method to...Ch. 3.8 - Approximating Reciprocals Use the result of...Ch. 3.8 - Using Newtons MethodExercises 2931 present...Ch. 3.8 - Using Newtons Method Exercises 29-31 present...Ch. 3.8 - Using Newtons Method Exercises 29-31 present...Ch. 3.8 - HOW DO YOU SEE IT? For what value(s) will Newtons...Ch. 3.8 - Mechanics Rule The Mechanics Rule for...Ch. 3.8 - Approximating Radicals (a) Use Newtons Method and...Ch. 3.8 - Newton's Method In your own words and using a...Ch. 3.8 - Crime The total number of arrests T (in thousands)...Ch. 3.8 - True or False? In Exercises 37-40, determine...Ch. 3.8 - True or False? In Exercises 3740, determine...Ch. 3.8 - True or False? In Exercises 3740, determine...Ch. 3.8 - True or False? In Exercises 3538, determine...Ch. 3.8 - Tangent Lines The graph of f(x)=sinx has...Ch. 3.8 - Point of Tangency The graph of f(x)=cosx and a...Ch. 3.9 - Using a Tangent Line Approximation In Exercises...Ch. 3.9 - Using a Tangent Line Approximation In Exercises...Ch. 3.9 - Using a Tangent Line Approximation In Exercises...Ch. 3.9 - Using a Tangent Line Approximation In Exercises...Ch. 3.9 - Using a Tangent Line Approximation In Exercises...Ch. 3.9 - Using a Tangent Line Approximation In Exercises...Ch. 3.9 - Comparing y and dy In Exercises 710, use the...Ch. 3.9 - Comparing y and dy In Exercises 1318, use the...Ch. 3.9 - Comparing y and dy In Exercises 1318, use the...Ch. 3.9 - Comparing y and dy In Exercises 1318, use the...Ch. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Finding a Differential In Exercises 19-28, find...Ch. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Finding a Differential In Exercises 19-28, find...Ch. 3.9 - Finding a Differential In Exercises 19-28, find...Ch. 3.9 - Using Differentials In Exercises 29 and 30, use...Ch. 3.9 - Using Differentials In Exercises 29 and 30, use...Ch. 3.9 - Using Differentials In Exercises 31 and 32, use...Ch. 3.9 - Using Differentials In Exercises 31 and 32, use...Ch. 3.9 - Area The measurement of the side of a square floor...Ch. 3.9 - Area The measurement of the radius of a circle is...Ch. 3.9 - Area The measurements of the base and altitude of...Ch. 3.9 - Circumference The measurement of the circumference...Ch. 3.9 - Volume and Surface Area The measurement of the...Ch. 3.9 - Volume and Surface Area The radius of a spherical...Ch. 3.9 - Stopping Distance The total stopping distance T of...Ch. 3.9 - HOW DO YOU SEE IT? The graph shows the profit P...Ch. 3.9 - Pendulum The period of a pendulum is given by...Ch. 3.9 - Ohms Law A current of I amperes passes through a...Ch. 3.9 - Projectile Motion The range R of a projectile is...Ch. 3.9 - Surveying A surveyor standing 50 feet from the...Ch. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - Verifying a Tangent Line Approximation In...Ch. 3.9 - Verifying a Tangent Line Approximation In...Ch. 3.9 - WRITING ABOUT CONCEPTS Comparing y and dy Describe...Ch. 3.9 - Describing Terms When using differentials, what is...Ch. 3.9 - Using Differentials In Exercises 45 and 46, give a...Ch. 3.9 - Using Differentials In Exercises 45 and 46, give a...Ch. 3.9 - True or False? In Exercises 4953, determine...Ch. 3.9 - True or False? In Exercises 4953, determine...Ch. 3.9 - True or False? In Exercises 4953, determine...Ch. 3.9 - True or False? In Exercises 49-53, determine...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Using Rolle's Theorem In Exercises 912, determine...Ch. 3 - Using Rolle's Theorem In Exercises 9-12, determine...Ch. 3 - Using Rolles Theorem In Exercises 9-12, determine...Ch. 3 - Using Rolles Theorem In Exercises 9-12, determine...Ch. 3 - Using the Mean Value Theorem In Exercises 13-18,...Ch. 3 - Using the Mean Value Theorem In Exercises 13-18,...Ch. 3 - Using the Mean Value Theorem In Exercises 13-18,...Ch. 3 - Using the Mean Value Theorem In Exercises 13-18,...Ch. 3 - Using the Mean Value Theorem In Exercises 13-18,...Ch. 3 - Using the Mean Value Theorem In Exercises 13-18,...Ch. 3 - Mean Value Theorem Can the Mean Value Theorem be...Ch. 3 - Using the Mean Value Theorem (a) For the function...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which f Is Increasing or Decreasing...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Think About It In Exercises 49 and 50, sketch the...Ch. 3 - Think About It In Exercises 49 and 50, sketch the...Ch. 3 - Writing A newspaper headline states that "The rate...Ch. 3 - Inventory Cost The cost of inventory C depends on...Ch. 3 - Modeling Data Outlays for national defense D (in...Ch. 3 - Modeling Data The manager of a store recorded the...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5362, find the limit....Ch. 3 - Finding a Limit In Exercises 5362, find the limit....Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 55-64, find the...Ch. 3 - Finding a Limit In Exercises 55-64, find the...Ch. 3 - Horizontal Asymptotes In Exercises 6366, use a...Ch. 3 - Finding Horizontal Asymptotes Using Technology In...Ch. 3 - Horizontal Asymptotes In Exercises 6366, use a...Ch. 3 - Horizontal Asymptotes In Exercises 6366, use a...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - 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Points of Intersection In Exercises 93 and 94,...Ch. 3 - Comparing y and dy In Exercises 91 and 92, use the...Ch. 3 - Comparing y and dy In Exercises 91 and 92, use the...Ch. 3 - Finding a Differential In Exercises 97 and 98,...Ch. 3 - Finding a Differential In Exercises 97 and 98,...Ch. 3 - Volume and Surface Area The radius of a sphere is...Ch. 3 - Demand Function A company finds that the demand...Ch. 3 - Relative Extrema Graph the fourth-degree...Ch. 3 - Relative Extrema (a) Graph the fourth-degree...Ch. 3 - Relative Minimum Let f(x)=cx+x2 Determine all...Ch. 3 - Points of Inflection (a) Let f(x)=ax2+bx+c,a0, be...Ch. 3 - Extended Mean Value Theorem Prove the Extended...Ch. 3 - Illumination The amount of illumination of a...Ch. 3 - Minimum Distance Consider a room in the shape of a...Ch. 3 - Areas of Triangles The line joining P and Q...Ch. 3 - Mean Value Theorem Determine the values a, b, and...Ch. 3 - Mean Value Theorem Determine the values a. b, c....Ch. 3 - Proof Let f and g be functions that are continuous...Ch. 3 - Proof (a) Prove that limxx2= (b) Prove that...Ch. 3 - Tangent Lines Find the point on the graph of...Ch. 3 - Stopping Distance The police department must...Ch. 3 - Darbouxs Theorem Prove Darbouxs Theorem: Let f be...Ch. 3 - Maximum Area The figures show a rectangle, a...Ch. 3 - Point of Inflection Show that the cubic polynomial...Ch. 3 - Minimum Length A legal-sized sheet of paper (8.5...Ch. 3 - Quadratic Approximation The polynomial...

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