Explanation Given information: The function: F ( x ) = x + 3 and a = 1 Calculation: We are given the function F ( x ) = x + 3 and a = 1 We know that for a function f ( x ) the linear approximation of the function at x = a is given by: f ( x ) ≈ f ( a ) + f ' ( a ) ( x − a ) The quadratic approximation of the function is given by: y = f ( a ) + f ' ( a ) ( x − a ) + 1 2 f ' ' ( a ) ( x − a ) 2 For the given f ( x ) : f ' ( x ) = 1 2 x + 3 → f ' ( 1 ) = 1 4

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ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Chapter 3.8, Problem 39E

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To find: the quadratic approximation to F(x)=x+3 near a = 1 and graph f , the quadratic approximation and the linear approximation from 1 on a common screen.

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Chapter 3.8, Problem 38E

Chapter 3.8, Problem 40E

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8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

8:39 *** TEMU 5G 60% A ferris wheel is 28 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the amplitude? 14 meters What is the equation of the Midline? y = 16 What is the period? 4 meters minutes The equation that models the height of the ferris wheel after t minutes is: f(t): = ƒ (3) = ·−14(0) + 16 syntax error: you gave an equation, not an expression. syntax error. Check your variables - you might be using an incorrect one. How high are you off of the ground after 3 minutes? Round your answe the nearest meter. ||| <

Chapter 3 Solutions

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the quadratic approximation to F ( x ) = x + 3 near a = 1 and graph f , the quadratic approximation and the linear approximation from 1 on a common screen.

Solution Summary: The author compares the quadratic and linear approximations of the functions on a common screen.

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To find: the quadratic approximation to F(x)=x+3 near a = 1 and graph f , the quadratic approximation and the linear approximation from 1 on a common screen.

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Chapter 3 Solutions