Use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic to show that fl(g(1.015)) is inaccurate, where xl/4 r!/4 – 1 - (x)6 x – 1 Derive the second order (n = 2) quadratic Taylor polynomial approximation for f(x) = x^1/4 , expanded about a = (a). 1, and use it to get an accurate approximation to g(x) in part Verify that your approximation in (b) is more accurate.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.5: Other Types Of Equations
Problem 56E
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a) Use base b= 10, precision k = 4, idealized, chopping floating-point arithmetic to show
that fl(g(1.015)) is inaccurate, where
xl/4
g(x) =
1
х — 1
b) Derive the second order (n = 2) quadratic Taylor polynomial approximation for f(x) =
x^1/4 , expanded about a = 1, and use it to get an accurate approximation to g(x) in part
(а).
c) Verify that your approximation in (b) is more accurate.
Transcribed Image Text:a) Use base b= 10, precision k = 4, idealized, chopping floating-point arithmetic to show that fl(g(1.015)) is inaccurate, where xl/4 g(x) = 1 х — 1 b) Derive the second order (n = 2) quadratic Taylor polynomial approximation for f(x) = x^1/4 , expanded about a = 1, and use it to get an accurate approximation to g(x) in part (а). c) Verify that your approximation in (b) is more accurate.
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