- #1
bcjochim07
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Taylor Polynomial Error--Please help!
Use Taylor's theorem to determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than .001.
e^.3
So is the procedure to take the derivatives and plug in 0 (since c=0) and find an expression for the n+1 derivative?
f'(c) = 1 f''(c)=1 f'''(c) =1 ...
so the n+1 derivative is 1
So Rn= 1/(n+1)! * (.3) ^(n+1)
Then I set up an equality to find n so that Rn < .001
and n = 3 ?
I want to be sure I am taking the right approach on these problems, so is this the way to do it?
Use Taylor's theorem to determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than .001.
e^.3
So is the procedure to take the derivatives and plug in 0 (since c=0) and find an expression for the n+1 derivative?
f'(c) = 1 f''(c)=1 f'''(c) =1 ...
so the n+1 derivative is 1
So Rn= 1/(n+1)! * (.3) ^(n+1)
Then I set up an equality to find n so that Rn < .001
and n = 3 ?
I want to be sure I am taking the right approach on these problems, so is this the way to do it?