Instead of approximating In x near x= 1, approximate In (1 + x) near x = 0 to obtain a simpler formula this way. (a) Find the linearization of In (1 + x) at x = 0. (b) Estimate the five decimal place error involved in replacing In (1 +x) with x on the interval [0,0.1]. (c) Graph In (1 +x) and x together for 0sxs0.5. Use different colors, if available. At what points does the approximation of In (1+x) seem the best? Least good? By reading coordinates from the graph, find as good an upper bound for the error as the graphing utility will allow.
Instead of approximating In x near x= 1, approximate In (1 + x) near x = 0 to obtain a simpler formula this way. (a) Find the linearization of In (1 + x) at x = 0. (b) Estimate the five decimal place error involved in replacing In (1 +x) with x on the interval [0,0.1]. (c) Graph In (1 +x) and x together for 0sxs0.5. Use different colors, if available. At what points does the approximation of In (1+x) seem the best? Least good? By reading coordinates from the graph, find as good an upper bound for the error as the graphing utility will allow.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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![Instead of approximating In x near x = 1, approximate In (1 +x) near x = 0 to obtain a simpler formula this way.
(a) Find the linearization of In (1 + x) at x = 0.
(b) Estimate the five decimal place error involved in replacing In (1 +x) with x on the interval [0,0.1].
(c) Graph In (1+x) and x together for 0 sxs0.5. Use different colors, if available. At what points does the approximation of In (1+x) seem the best?
Least good? By reading coordinates from the graph, find as good an upper bound for the error as the graphing utility will allow.
(a) The linearization of In (1 +x) at x = 0 is L(x) .
(b) The approximation error is
(Round to five decimal places as needed.)
(c) Choose the correct graph of y = In (1 +x) and y =x shown both for 0sxs0.5.
O A.
В.
O D.
Q
65
Find the x-value in the interval 0sxs0.5 at which the approximation of In (1 +x) seems the best. Choose the correct answer below.
O A. 0.2
O B. 0.3
OC. 0
O D. 0.5
Find the x-value in the interval 0sxs0.5 at which the approximation of In (1 +x) seems the least good. Choose the correct answer below.
O A. 0.1
O B. 0.2
O C. 0.4
O D. 0.5
By reading the coordinates from the graph, the upper bound for the error is|
(Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc533774-2db2-4c40-ad62-e47c502b55d9%2Fb697db33-7da8-494c-a4a6-82b427aa4bf0%2Ftxhiqyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Instead of approximating In x near x = 1, approximate In (1 +x) near x = 0 to obtain a simpler formula this way.
(a) Find the linearization of In (1 + x) at x = 0.
(b) Estimate the five decimal place error involved in replacing In (1 +x) with x on the interval [0,0.1].
(c) Graph In (1+x) and x together for 0 sxs0.5. Use different colors, if available. At what points does the approximation of In (1+x) seem the best?
Least good? By reading coordinates from the graph, find as good an upper bound for the error as the graphing utility will allow.
(a) The linearization of In (1 +x) at x = 0 is L(x) .
(b) The approximation error is
(Round to five decimal places as needed.)
(c) Choose the correct graph of y = In (1 +x) and y =x shown both for 0sxs0.5.
O A.
В.
O D.
Q
65
Find the x-value in the interval 0sxs0.5 at which the approximation of In (1 +x) seems the best. Choose the correct answer below.
O A. 0.2
O B. 0.3
OC. 0
O D. 0.5
Find the x-value in the interval 0sxs0.5 at which the approximation of In (1 +x) seems the least good. Choose the correct answer below.
O A. 0.1
O B. 0.2
O C. 0.4
O D. 0.5
By reading the coordinates from the graph, the upper bound for the error is|
(Round to four decimal places as needed.)
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