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Solution: Taylor polynomials centered at a 0a. Find the
Chapter 7, Problem 30E(choose chapter or problem)
Taylor polynomials centered at \(a \neq 0\)
a. Find the nth-order Taylor polynomials for the given function centered at the given point a for n = 0, 1, and 2.
b. Graph the Taylor polynomials and the function.
\(f(x)=\sqrt[3]{x}, a=8\)
Questions & Answers
QUESTION:
Taylor polynomials centered at \(a \neq 0\)
a. Find the nth-order Taylor polynomials for the given function centered at the given point a for n = 0, 1, and 2.
b. Graph the Taylor polynomials and the function.
\(f(x)=\sqrt[3]{x}, a=8\)
ANSWER:Solution 30EStep 1:In this problem we have to find the nth-order Taylor polynomials for centered at the point for n = 0, 1, and 2Taylor series is given by Let us first find order Taylor polynomial.In our case, That is So, what we need to do to get desired polynomial is to calculate derivatives, evaluate them at the given point and plug results into given formula.Then Now use calculated values in to get the polynomial. Thus Taylor polynomial of upto with center is