1. Suppose we would like to approximate V10 using the Taylor polynomial of order 3 for the function f(x) = Vx centered at a. n = 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.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Suppose we would like to approximate V10 using the Taylor polynomial of order
3 for the function f(x) = V centered at a.
n =
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.
Transcribed Image Text:1. Suppose we would like to approximate V10 using the Taylor polynomial of order 3 for the function f(x) = V centered at a. n = 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.
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