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## Homework Statement

Let f be a function whose seventh derivative is f

^{7}(x) = 10,000cos x. If x = 1 is in the interval of convergence of the power series for this function, then the Taylor polynomial of degree six centered at x = 0 will approximate f(1) with an error of not more than

a.) 2.45 x 10

_{-5}

b.) 1.98 x 10

^{-4}

c.) 3.21 x 10

^{-2}

d.) 0.248

e.) 1.984

## Homework Equations

The Lagrange Remainder Formula, it states that the biggest error is only as large as the next sum in the series.

The formula is:

R

_{n}[tex]\leq[/tex][tex]\frac{f^{7}(z)(x-c)^7}{(n+1)!}[/tex]

## The Attempt at a Solution

The maximum error is the next term in the sequence. Looking at the lagrange formula, we're looking for the maximum error, or the f

^{7}(z) term. Since we are given f

^{7}(x) = 10,000cos x and given that x = 1 is in the interval of convergence... I assumed that f

^{7}(1) = 10,000cos(1) is the maximum error.

Plugging it back in the LaGrange Formula I get the following:

R

_{6}[tex]\leq[/tex] [tex]\frac{f^{7}(z)x^7}{7!}[/tex] = [tex]\frac{10000cos 1}{7!}[/tex]

I get a number that is not in the multiple choice answers. Any tips/ideas? Thanks