a. Answer x = 3.33 Explanation Given information: Consider the function f ( x ) = 3 sin ( 0.6 x − 2 ) .Approximate the zero of the function in the interval [ 0 , 6 ] . Calculation: Consider the function, f ( x ) = 3 sin ( 0.6 x − 2 ) To find the zero of the function solve f ( x ) = 0 , f o r , x . f ( x ) = 0 3 sin ( 0.6 x − 2 ) = 0 sin ( 0.6 x − 2 ) = 0 sin ( 0.6 x − 2 ) = sin 0 0.6 x − 2 = 0 x = 2 0.6 x = 3.33 Hence, the zero of the function in the interval [ 0 , 6 ] is x = 3.33 b. To determine Use a graphing utility to graph f and g in the same viewing window. Answer Explanation Given information: Consider the function f ( x ) = 3 sin ( 0.6 x − 2 ) .A quadratic approximation agreeing with f at x = 5 is g ( x ) = − 0.45 x 2 + 5.52 x − 13.70 Calculation: Consider the function, agreeing with f at x = 5 g ( x ) = − 0.45 x 2 + 5.52 x − 13.70 Use T I − 83 calculator to graph f and g Step1. Press Y = enter the f and g display is as shown, Step2. Press WINDOW button and set the range of the axis, the display is as shown, Step3. Press GRAPH button to plot the graph of f and g display is as shown, Step4. Find the value of the function f and g at x = 5 Press 2 n d and then TRACE button and select: 1 value and press enter Hence, the value of the function f and g at x = 5 are nearly equal. c. To determine Use the Quadratic Formula to find the zeros of g . Answer x = 8.811 x = 3.455 Explanation Given information: Consider the function f ( x ) = 3 sin ( 0.6 x − 2 ) . Use the Quadratic Formula to find the zeros of g . Compare the zero of g in the interval [ 0 , 6 ] with the result of part ( a ) . Calculation: Consider the function, g ( x ) = − 0.45 x 2 + 5.52 x − 13.70 Use quadratic formula to find the zero of g . x = − b ± b 2 − 4 a c 2 a = − 5.52 ± ( − 5.52 ) 2 − 4 ( − 0.45 ) ( − 13.70 ) 2 ( − 0.45 ) = − 5.52 ± 30.4704 − 24.66 − 0.9 = − 5.52 ± 2.41048 − 0.9 = 8.811 , 3.455 Hence, the zeroes of the function are x = 8.811 x = 3.455 root of function g is 3.455 which is closer to root of function f is 3.33 .

3rd Edition

ISBN: 9781133947202

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 5.3, Problem 96E

To determine

Approximate the zero of the function in the interval [0,6] .

Expert Solution

Answer to Problem 96E

x=3.33

Explanation of Solution

Given information:

Consider the function f(x)=3sin(0.6x−2) .Approximate the zero of the function in the interval [0,6] .

Calculation:

Consider the function,

f(x)=3sin(0.6x−2)

To find the zero of the function solve f(x)=0,for,x .

f(x)=03sin(0.6x−2)=0sin(0.6x−2)=0sin(0.6x−2)=sin00.6x−2=0x=20.6x=3.33

Hence, the zero of the function in the interval [0,6] is x=3.33

To determine

Use a graphing utility to graph f and g in the same viewing window.

Expert Solution

Answer to Problem 96E

Precalculus with Limits, Chapter 5.3, Problem 96E , additional homework tip 1

Explanation of Solution

Given information:

Consider the function f(x)=3sin(0.6x−2) .A quadratic approximation agreeing with f at x=5 is

g(x)=−0.45x2+5.52x−13.70

Calculation:

Consider the function, agreeing with f at x=5

g(x)=−0.45x2+5.52x−13.70

Use TI−83 calculator to graph f and g

Step1. Press Y= enter the f and g display is as shown,

Precalculus with Limits, Chapter 5.3, Problem 96E , additional homework tip 2

Step2. Press WINDOW button and set the range of the axis, the display is as shown,

Precalculus with Limits, Chapter 5.3, Problem 96E , additional homework tip 3

Step3. Press GRAPH button to plot the graph of f and g display is as shown,

Precalculus with Limits, Chapter 5.3, Problem 96E , additional homework tip 4

Step4. Find the value of the function f and g at x=5

Press 2nd and then TRACE button and select: 1 value and press enter

Precalculus with Limits, Chapter 5.3, Problem 96E , additional homework tip 5

Hence, the value of the function f and g at x=5 are nearly equal.

To determine

Use the Quadratic Formula to find the zeros of g .

Expert Solution

Answer to Problem 96E

x=8.811x=3.455

Explanation of Solution

Given information:

Consider the function f(x)=3sin(0.6x−2) .

Use the Quadratic Formula to find the zeros of g . Compare the zero of g in the interval [0,6] with the result of part (a) .

Calculation:

Consider the function,

g(x)=−0.45x2+5.52x−13.70

Use quadratic formula to find the zero of g .

x=−b±b2−4ac2a=−5.52±(−5.52)2−4(−0.45)(−13.70)2(−0.45)=−5.52±30.4704−24.66−0.9=−5.52±2.41048−0.9=8.811,3.455

Hence, the zeroes of the function are x=8.811x=3.455 root of function g is 3.455 which is closer to root of function f is 3.33 .

Chapter 5.3, Problem 95E

Chapter 5.3, Problem 97E

Chapter 5 Solutions

Precalculus with Limits

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