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Solved: Taylor polynomials centered at a ? 0a. Find the
Chapter 7, Problem 28E(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.
\(f(x)=\cos x, a=\pi / 6\)
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.
\(f(x)=\cos x, a=\pi / 6\)
ANSWER:Solution 28E
Step 1:
In this problem we have to find the nth-order Taylor polynomials for cos x centered at the point for n = 0, 1, and 2
Taylor 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