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Solved: Alternative approach Compute the coefficients for
Chapter 8, Problem 63E(choose chapter or problem)
Alternative approach Compute the coefficients for the Taylor series for the following functions about the given point a and then use the first four terms of the series to approximate the given number.
\(f(x)=\sqrt[4]{x}\) with a = 16; approximate \(\sqrt[4]{13}\).
Questions & Answers
QUESTION:
Alternative approach Compute the coefficients for the Taylor series for the following functions about the given point a and then use the first four terms of the series to approximate the given number.
\(f(x)=\sqrt[4]{x}\) with a = 16; approximate \(\sqrt[4]{13}\).
ANSWER:Solution 63E
Step 1:
In this problem we need to find the coefficients for the Taylor series for the function with and then we have to approximate
The -order Taylor polynomial for y = f(x) at is:
It can also be written in sigma notation as follows,
where the constants is the Taylor coefficient of about .