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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 8.4, Problem 41E

Textbook Problem

**Slope of a Tangent Line** In Exercises 41 and 42, find the slope of the tangent line to the given sine function at the origin. What can you conclude about the slope of the sine function sin ax at the origin?

Calculus: An Applied Approach (MindTap Course List)

Ch. 8.1 - For each angle, find a coterminal angle such that...Ch. 8.1 - Convert each degree measure to radian measure. a....Ch. 8.1 - Convert each radian measure to degree measure. a....Ch. 8.1 - Find the area of an isosceles right triangle with...Ch. 8.1 - In Exercises 1 and 2, find the area of the...Ch. 8.1 - In Exercises 1 and 2, find the area of the...Ch. 8.1 - In Exercises 36, let a and b represent the lengths...Ch. 8.1 - In Exercises 36, let a and b represent the lengths...Ch. 8.1 - In Exercises 36, let a and b represent the lengths...Ch. 8.1 - In Exercises 36, let a and b represent the lengths...

Ch. 8.1 - In Exercises 36, let a and b represent the lengths...Ch. 8.1 - In Exercises 710, show that the points form the...Ch. 8.1 - In Exercises 710, show that the points form the...Ch. 8.1 - In Exercises 710, show that the points form the...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Conterminal Angles In Exercise 7-10,...Ch. 8.1 - Finding Conterminal Angles In Exercise 7-10,...Ch. 8.1 - Finding Conterminal Angles In Exercise 7-10,...Ch. 8.1 - Finding Conterminal Angles In Exercise 7-10,...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Finding the Area of an Equilateral Triangle In...Ch. 8.1 - Finding the Area of an Equilateral Triangle In...Ch. 8.1 - Finding the Area of an Equilateral Triangle In...Ch. 8.1 - Finding the Area of an Equilateral Triangle In...Ch. 8.1 - Height A person 6 feet tall standing 16 feet from...Ch. 8.1 - Length A guy wire is stretched from a broadcasting...Ch. 8.1 - Arc Length In Exercises 47-50, use the following...Ch. 8.1 - Arc Length In Exercises 47-50, use the following...Ch. 8.1 - Arc Length In Exercises 47-50, use the following...Ch. 8.1 - Arc Length In Exercises 47-50, use the following...Ch. 8.1 - Speed of Revolution A Blu-ray disc can have an...Ch. 8.1 - How do you see it? Determine which angles in the...Ch. 8.1 - Area of a Sector of a Circle In Exercises 53 and...Ch. 8.1 - Area of a Sector of a Circle In Exercises 53 and...Ch. 8.1 - True or False? In Exercises 55-58, determine...Ch. 8.1 - True or False? In Exercises 55-58, determine...Ch. 8.1 - True or False? In Exercises 55-58, determine...Ch. 8.1 - True or False? In Exercises 55-58, determine...Ch. 8.2 - Let (3,1) be a point on the terminal side of , as...Ch. 8.2 - Evaluate each trigonometric function. a. sin56 b....Ch. 8.2 - Evaluate each trigonometric function. a. sin(6) b....Ch. 8.2 - Find the height of a building that casts a 75-foot...Ch. 8.2 - When the object in Example 5 is 4 feet from the...Ch. 8.2 - Solve for in each equation. Assume 02. a. cos=22...Ch. 8.2 - Solve the equation for . sin2+sin=0,02Ch. 8.2 - In Exercises 1-4, simplify the expression. 72+242Ch. 8.2 - In Exercises 1-4, simplify the expression....Ch. 8.2 - In Exercises 1-4, simplify the expression. 6222Ch. 8.2 - In Exercises 1-4, simplify the expression. 9232Ch. 8.2 - In Exercises 5-8, convert the degree measure to...Ch. 8.2 - In Exercises 5-8, convert the degree measure to...Ch. 8.2 - In Exercises 5-8, convert the degree measure to...Ch. 8.2 - In Exercises 5-8, convert the degree measure to...Ch. 8.2 - In Exercises 9-12, solve the equation. x2x=0Ch. 8.2 - In Exercises 9-12, solve the equation. 2x2+x=0Ch. 8.2 - In Exercises 9-12, solve the equation. x22x=3Ch. 8.2 - In Exercises 9-12, solve the equation. x25x=6Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Length A 20-foot ladder leaning against the side...Ch. 8.2 - Width of a River A biologist wants to know the...Ch. 8.2 - Distance An airplane flying at an altitude of 6...Ch. 8.2 - Skateboard Ramp A skateboard ramp with a height of...Ch. 8.2 - Height A 25-meter line is used to tether a...Ch. 8.2 - Empire State Building You are standing 45 meters...Ch. 8.2 - Loading Ramp A ramp 1712 feet in length rises to a...Ch. 8.2 - Height The height of a building is 180 feet. Find...Ch. 8.2 - Height of a Mountain In traveling across flat...Ch. 8.2 - HOW DO YOU SEE IT? Consider an angle in standard...Ch. 8.2 - Medicine The temperature T (in degrees Fahrenheit)...Ch. 8.2 - Sales A company that produces a window and door...Ch. 8.2 - Using the Value of a Trigonometric Function In...Ch. 8.2 - Using the Value of a Trigonometric Function In...Ch. 8.2 - True or False? In Exercises 85-88, determine...Ch. 8.2 - True or False? In Exercises 85-88, determine...Ch. 8.2 - True or False? In Exercises 85-88, determine...Ch. 8.2 - True or False? In Exercises 85-88, determine...Ch. 8.3 - Sketch the graph of g(x)=2cosx.Ch. 8.3 - Sketch the graph of g(x)=2sin4x.Ch. 8.3 - Sketch the graph of g(x)=tan4x.Ch. 8.3 - Evaluate the function f(x)=1cosxx at several...Ch. 8.3 - Checkpoint 5 Worked-out solution available at...Ch. 8.3 - Checkpoint 6 Worked-out solution available at...Ch. 8.3 - In Exercises 1 and 2, find the limit....Ch. 8.3 - In Exercises 1 and 2, find the limit....Ch. 8.3 - In Exercises 3-10, evaluate the trigonometric...Ch. 8.3 - In Exercises 3-10, evaluate the trigonometric...Ch. 8.3 - In Exercises 3-10, evaluate the trigonometric...Ch. 8.3 - In Exercises 3-10, evaluate the trigonometric...Ch. 8.3 - In Exercises 3-10, evaluate the trigonometric...Ch. 8.3 - In Exercises 3-10, evaluate the trigonometric...Ch. 8.3 - In Exercises 3-10, evaluate the trigonometric...Ch. 8.3 - In Exercises 3-10, evaluate the trigonometric...Ch. 8.3 - In Exercises 11-18, use a calculator to evaluate...Ch. 8.3 - In Exercises 11-18, use a calculator to evaluate...Ch. 8.3 - In Exercises 11-18, use a calculator to evaluate...Ch. 8.3 - In Exercises 11-18, use a calculator to evaluate...Ch. 8.3 - In Exercises 11-18, use a calculator to evaluate...Ch. 8.3 - In Exercises 11-18, use a calculator to evaluate...Ch. 8.3 - In Exercises 11-18, use a calculator to evaluate...Ch. 8.3 - In Exercises 11-18, use a calculator to evaluate...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Evaluating a Trigonometric Limit In Exercises...Ch. 8.3 - Graphical Reasoning In Exercises 63-66, find a and...Ch. 8.3 - Graphical Reasoning In Exercises 63-66, find a and...Ch. 8.3 - Graphical Reasoning In Exercises 63-66, find a and...Ch. 8.3 - Graphical Reasoning In Exercises 63-66, find a and...Ch. 8.3 - Phase Shift In Exercises 67-70, match the function...Ch. 8.3 - Phase Shift In Exercises 6770, match the function...Ch. 8.3 - Phase Shift In Exercises 6770, match the function...Ch. 8.3 - Phase Shift In Exercises 6770, match the function...Ch. 8.3 - Writing an Equation In Exercises 71 and 72, write...Ch. 8.3 - Writing an Equation In Exercises 71 and 72, write...Ch. 8.3 - Biology: Predator-Prey Cycle The population P of a...Ch. 8.3 - Biology: Predator-Prey Cycle The population P of a...Ch. 8.3 - Music When tuning a piano, a technician strikes a...Ch. 8.3 - Health The function P=10020cos5t3 approximates the...Ch. 8.3 - Health For a person at rest, the velocity v (in...Ch. 8.3 - Health After a person exercises for a few minutes,...Ch. 8.3 - Transportation Workers The number W (in thousands)...Ch. 8.3 - Sales The snowmobile sales 5 (in units) at a...Ch. 8.3 - Physics Use the graphs below to answer each...Ch. 8.3 - Think About It Consider the function given by...Ch. 8.3 - Think About It Consider the functions given by...Ch. 8.3 - HOW DO YOU SEE IT? The normal monthly high...Ch. 8.3 - True or False? In Exercises 8588, determine...Ch. 8.3 - True or False? In Exercises 85-88, determine...Ch. 8.3 - True or False? In Exercises 85-88, determine...Ch. 8.3 - True or False? In Exercises 85-88, determine...Ch. 8.3 - In Exercises 14, convert the degree measure to...Ch. 8.3 - In Exercises 14, convert the degree measure to...Ch. 8.3 - In Exercises 14, convert the degree measure to...Ch. 8.3 - In Exercises 14, convert the degree measure to...Ch. 8.3 - In Exercises 58, convert the radian measure to...Ch. 8.3 - In Exercises 58, convert the radian measure to...Ch. 8.3 - In Exercises 58, convert the radian measure to...Ch. 8.3 - In Exercises 58, convert the radian measure to...Ch. 8.3 - In Exercises 914, evaluate the trigonometric...Ch. 8.3 - In Exercises 914, evaluate the trigonometric...Ch. 8.3 - In Exercises 914, evaluate the trigonometric...Ch. 8.3 - In Exercises 914, evaluate the trigonometric...Ch. 8.3 - In Exercises 914, evaluate the trigonometric...Ch. 8.3 - In Exercises 914, evaluate the trigonometric...Ch. 8.3 - In Exercises 15-17, solve the equation for ....Ch. 8.3 - In Exercises 15-17, solve the equation for ....Ch. 8.3 - In Exercises 15-17, solve the equation for ....Ch. 8.3 - In Exercises 18-20, solve the triangle for the...Ch. 8.3 - In Exercises 18-20, solve the triangle for the...Ch. 8.3 - In Exercises 1820, solve the triangle for the...Ch. 8.3 - A map maker needs to determine the distance d...Ch. 8.3 - In Exercises 22-24, (a) find the period of the...Ch. 8.3 - In Exercises 22-24, (a) find the period of the...Ch. 8.3 - In Exercises 22-24, (a) find the period of the...Ch. 8.3 - A company that produces snowboards forecasts...Ch. 8.4 - Differentiate each function. a. y=cos4x b....Ch. 8.4 - Differentiate each function. a. f(x)=2cosx3 b....Ch. 8.4 - Differentiate each function. a. y=sec4x b. y=cotx2Ch. 8.4 - Differentiate each function. a. f(x)=cos2x b....Ch. 8.4 - Differentiate each function. a. y=x2cosx b....Ch. 8.4 - Find the relative extrema of y=x2cosx in the...Ch. 8.4 - Find the relative extrema of y=12sin2x+cosx on the...Ch. 8.4 - Using the model from Example 8, find the rate at...Ch. 8.4 - Checkpoint 9 Worked-out solution available at...Ch. 8.4 - In Exercises 1-4, find the derivative of the...Ch. 8.4 - In Exercises 1-4, find the derivative of the...Ch. 8.4 - In Exercises 1-4, find the derivative of the...Ch. 8.4 - In Exercises 1-4, find the derivative of the...Ch. 8.4 - In Exercises 5 and 6, find all relative extrema of...Ch. 8.4 - In Exercises 5 and 6, find all relative extrema of...Ch. 8.4 - In Exercises 7-10, solve the equation for x....Ch. 8.4 - In Exercises 7-10, solve the equation for x....Ch. 8.4 - In Exercises 7-10, solve the equation for x....Ch. 8.4 - In Exercises 710, solve the equation for x. 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The graph shows the height h...Ch. 8.4 - Analyzing a Function In Exercises 75-80, use a...Ch. 8.4 - Analyzing a Function In Exercises 75-80, use a...Ch. 8.4 - Analyzing a Function In Exercises 75-80, use a...Ch. 8.4 - Analyzing a Function In Exercises 75-80, use a...Ch. 8.4 - Analyzing a Function In Exercises 75-80, use a...Ch. 8.4 - Analyzing a Function In Exercises 75-80, use a...Ch. 8.4 - True or False? In Exercises 81 84, determine...Ch. 8.4 - True or False? In Exercises 81 84, determine...Ch. 8.4 - True or False? In Exercises 81 84, determine...Ch. 8.4 - True or False? 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