Math

CalculusCalculus: An Applied Approach (MindTap Course List)Analyzing a Function In Exercises 75-80, use a graphing utility to (a) graph f and f’ in the same viewing window over the specified interval, (b) find the critical numbers of f , (c) find the open interval(s) on which f' is positive and the open interval(s) on which f' is negative, and (d) find the relative extrema in the interval. Function Interval f ( x ) = sin x − 1 3 sin3 x + 1 5 sin5 x ( 0 , π )BuyFind*launch*

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 8.4, Problem 77E

Textbook Problem

**Analyzing a Function** In Exercises 75-80, use a graphing utility to (a) graph *f* and *f’* in the same viewing window over the specified interval, (b) find the critical numbers of *f*, (c) find the open interval(s) on which *f'* is positive and the open interval(s) on which *f'* is negative, and (d) find the relative extrema in the interval.

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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...

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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 - 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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 - 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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 - 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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? 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Assume...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Slope of a Tangent Line In Exercises 41 and 42,...Ch. 8.4 - Slope of a Tangent Line In Exercises 41 and 42,...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Implicit Differentiation In Exercises 51 and 52,...Ch. 8.4 - Implicit Differentiation In Exercises 51 and 52,...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Second Derivatives In Exercises 6366, find...Ch. 8.4 - Finding Second Derivatives In Exercises 6366, find...Ch. 8.4 - Finding Second Derivatives In Exercises 6366, find...Ch. 8.4 - Finding Second Derivatives In Exercises 6366, find...Ch. 8.4 - Meteorology The normal average daily temperature...Ch. 8.4 - Meteorology The number of hours of daylight D in...Ch. 8.4 - Transportation Workers The number W (in thousands)...Ch. 8.4 - Employment The number W (in thousands) of golf...Ch. 8.4 - Biology Plants do not grow at constant rates...Ch. 8.4 - Tides Throughout the day, the depth of water D (in...Ch. 8.4 - Think About It Rewrite the trigonometric function...Ch. 8.4 - HOW DO YOU SEE IT? 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? In Exercises 81 84, determine...Ch. 8.5 - Find 5sinxdx.Ch. 8.5 - Find each indefinite integral. a. 4x3cosx4dx b....Ch. 8.5 - Find 2csc2xcot2xdx.Ch. 8.5 - Find cos32xsin2xdx.Ch. 8.5 - Find cosxsinxdx.Ch. 8.5 - Find 0/2sin2xdxCh. 8.5 - Find the area of the region bounded by the graphs...Ch. 8.5 - Find sec2xdx.Ch. 8.5 - Use the temperature function T in Example 9 to...Ch. 8.5 - In Exercise 1-8, evaluate the trigonometric...Ch. 8.5 - In Exercise 1-8, evaluate the trigonometric...Ch. 8.5 - In Exercise 1-8, evaluate the trigonometric...Ch. 8.5 - In Exercise 1-8, evaluate the trigonometric...Ch. 8.5 - In Exercise 1-8, evaluate the trigonometric...Ch. 8.5 - In Exercise 1-8, evaluate the trigonometric...Ch. 8.5 - In Exercise 1-8, evaluate the trigonometric...Ch. 8.5 - In Exercise 1-8, evaluate the trigonometric...Ch. 8.5 - In Exercises 9-16, simplify the expression using...Ch. 8.5 - In Exercises 9-16, simplify the expression using...Ch. 8.5 - In Exercises 9-16, simplify the expression using...Ch. 8.5 - 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Transportation Workers The number W (In thousands)...Ch. 8.5 - Cost The temperature T (in degrees Fahrenheit) in...Ch. 8.5 - Water Supply The flow rate R (in thousands of...Ch. 8.5 - Sales In Example 8 in Section 8.4, the sales of a...Ch. 8.5 - HOW DO YOU SEE IT? 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