Edgar the engineer uses many complicated equations in his work. Before doing lengthy and time consuming calculations he often uses a linear approximation to investigate the problem. Edgar's current project requires the error in making this approximation to be less than 1 to provide valid results. In this instance, Edgar is working with the function h(x) = 100 + 3x sin 18 Let P(x) be the linear approximation of h(x) at x = 3. (a) Find P(x). Show full working.
Edgar the engineer uses many complicated equations in his work. Before doing lengthy and time consuming calculations he often uses a linear approximation to investigate the problem. Edgar's current project requires the error in making this approximation to be less than 1 to provide valid results. In this instance, Edgar is working with the function h(x) = 100 + 3x sin 18 Let P(x) be the linear approximation of h(x) at x = 3. (a) Find P(x). Show full working.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![. Edgar the engineer uses many complicated equations in his work. Before doing lengthy and time
consuming calculations he often uses a linear approximation to investigate the problem. Edgar's
current project requires the error in making this approximation to be less than 1 to provide valid
results. In this instance, Edgar is working with the function
h(x) :
= 100 + 3x sin
Let P(x) be the linear approximation of h(x) at x = 3.
(a) Find P(x). Show full working.
(b) To check the accuracy of Edgar's approximation, divide the interval [-0.2, 6.6] into halves to
obtain 3 x-values (including the end points). Create an Excel spreadsheet called Values and
enter
your name, Student ID and question number, then repeat the process from question 2(a).
(c) Copy and paste the cells from the Values sheet into a new spreadsheet and name it Formulas.
Convert this sheet so that it displays as formulas (as in question 2) ensuring that the columns are
wide enough to display the formulas fully. Submit screenshots of both the Values and Formulas
spreadsheets as part of your assignment. Please ensure that each sheet fits onto a single page.
(d) Now use the Desmos graphics calculator to display the graphs of y = h(x) and y = P(x). Include
DESMOS labels showing the points (x, h(x)) for the 3 equally-spaced x-values considered in
the spreadsheet in Question 3(b). Submit a screenshot of your Desmos graph (including the
formulas) as part of your assignment.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d6686f0-24e3-43de-bc21-a827730605bb%2F1c4702af-d0ec-4903-bde7-32b7f99c1a88%2F8zwypox_processed.png&w=3840&q=75)
Transcribed Image Text:. Edgar the engineer uses many complicated equations in his work. Before doing lengthy and time
consuming calculations he often uses a linear approximation to investigate the problem. Edgar's
current project requires the error in making this approximation to be less than 1 to provide valid
results. In this instance, Edgar is working with the function
h(x) :
= 100 + 3x sin
Let P(x) be the linear approximation of h(x) at x = 3.
(a) Find P(x). Show full working.
(b) To check the accuracy of Edgar's approximation, divide the interval [-0.2, 6.6] into halves to
obtain 3 x-values (including the end points). Create an Excel spreadsheet called Values and
enter
your name, Student ID and question number, then repeat the process from question 2(a).
(c) Copy and paste the cells from the Values sheet into a new spreadsheet and name it Formulas.
Convert this sheet so that it displays as formulas (as in question 2) ensuring that the columns are
wide enough to display the formulas fully. Submit screenshots of both the Values and Formulas
spreadsheets as part of your assignment. Please ensure that each sheet fits onto a single page.
(d) Now use the Desmos graphics calculator to display the graphs of y = h(x) and y = P(x). Include
DESMOS labels showing the points (x, h(x)) for the 3 equally-spaced x-values considered in
the spreadsheet in Question 3(b). Submit a screenshot of your Desmos graph (including the
formulas) as part of your assignment.
Transcribed Image Text:(e) Briefly comment (two or three sentences) on what conclusion (if any) can be made by looking at
the spreadsheet in Question 3(b) and Desmos graph in Question 3 (d) about whether or not the
error meets Edgar's requirement to use the linear approximation.
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