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carlodelmundo
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Homework Statement
Let f be a function whose seventh derivative is f7(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:
Rn [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 f7(z) term. Since we are given f7(x) = 10,000cos x and given that x = 1 is in the interval of convergence... I assumed that f7(1) = 10,000cos(1) is the maximum error.
Plugging it back in the LaGrange Formula I get the following:
R6 [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