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(a) Approximate the value of In(2) by (i) using z = 1 in the Maclaurin polynomial of degree 3 of In(1+1). (ii) Using z = -0.5 in your polynomial from part (i) (you should be able to relate the two with log rules). (iii) Compare your results in (i) and (ii) with the calculator value for In (2). (b) Using Taylor's inequality, show that both approximations to In(2) yield the same upper bound for the error despite the fact that one of the approximations is clearly better. (You should be calculating two separate upper bounds, one for z = 1 and one for z = -0.5.)

(a) Approximate the value of In(2) by (i) using z = 1 in the Maclaurin polynomial of degree 3 of In(1+1). (ii) Using z = -0.5 in your polynomial from part (i) (you should be able to relate the two with log rules). (iii) Compare your results in (i) and (ii) with the calculator value for In (2). (b) Using Taylor's inequality, show that both approximations to In(2) yield the same upper bound for the error despite the fact that one of the approximations is clearly better. (You should be calculating two separate upper bounds, one for z = 1 and one for z = -0.5.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. (a) Approximate the value of ln(2) by Bounded by 81921 (i) using z = 1 in the Maclaurin polynomial of degree 3 of In(1+x). (ii) Using r = -0.5 in your polynomial from part (i) (you should be able to relate the two with log rules). (iii) Compare your results in (i) and (ii) with the calculator value for In (2). (b) Using Taylor's inequality, show that both approximations to In(2) yield the same upper bound for the error despite the fact that one of the approximations is clearly better. (You should be calculating two separate upper bounds, one for x = 1 and one for x = -0.5.)
Transcribed Image Text:2. (a) Approximate the value of ln(2) by Bounded by 81921 (i) using z = 1 in the Maclaurin polynomial of degree 3 of In(1+x). (ii) Using r = -0.5 in your polynomial from part (i) (you should be able to relate the two with log rules). (iii) Compare your results in (i) and (ii) with the calculator value for In (2). (b) Using Taylor's inequality, show that both approximations to In(2) yield the same upper bound for the error despite the fact that one of the approximations is clearly better. (You should be calculating two separate upper bounds, one for x = 1 and one for x = -0.5.)
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