Problem D please 1. Suppose we would like to approximate V10 using the Taylor polynomial of ordern = 3 for the function f(x) = Yx centered at a.a) Identify a good choice for the center a.Hint: Look for a perfect cube close to 10.b) Find p3(x) and use it to approximate V10.c) Find the absolute error of the approximation by assuming the exact value of V10is given by a calculator.d) Does the p3(x) you found provide a better approximation of V10 or of V11?Explain your answer.

From part b:f(x)≈p3(x)=2+112(x-8)-1288(x-8)2+520736(x-8)3 Using this polynomial we get the…

Answered: d) Does the p3(x) you found provide a…

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d) Does the p3(x) you found provide a better approximation of V10 or of 11? Explain your answer.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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Question

Problem D please

1. Suppose we would like to approximate V10 using the Taylor polynomial of order
n = 3 for the function f(x) = Yx centered at a.
a) Identify a good choice for the center a.
Hint: Look for a perfect cube close to 10.
b) Find p3(x) and use it to approximate V10.
c) Find the absolute error of the approximation by assuming the exact value of V10
is given by a calculator.
d) Does the p3(x) you found provide a better approximation of V10 or of V11?
Explain your answer.

Expert Solution

Step 1

$From part b : f (x) \approx p_{3} (x) = 2 + \frac{1}{12} (x - 8) - \frac{1}{288} {(x - 8)}^{2} + \frac{5}{20736} {(x - 8)}^{3} Using this polynomial we get the approximation of \sqrt[3]{10} and \sqrt[3]{11} are : p_{3} (10) = 2 + \frac{1}{12} (10 - 8) - \frac{1}{288} {(10 - 8)}^{2} + \frac{5}{20736} {(10 - 8)}^{3} = \frac{5585}{2592} p_{3} (11) = 2 + \frac{1}{12} (11 - 8) - \frac{1}{288} {(11 - 8)}^{2} + \frac{5}{20736} {(11 - 8)}^{3} = \frac{1709}{768}$

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