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Lo.Lee.Ta.
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Homework Statement
a. Compute the second order Taylor polynomial centered at 2, P2(x), for the function ln(x).
b. Estimate the maximum error of the answer to part a for x in the interval [1,2].
Homework Equations
The Attempt at a Solution
For part a, I'm thinking that when it says "second order Taylor polynomial," it's talking about writing out the terms to the second derivative... Is that right?
c0 = f(0)(x) = ln(x) → ln(x)/0!
c1 = f(1)(x) = 1/x → 1/x/(1!)
c2 = f(2)(x) = -1/x2 → -1/x2/(2!) = -1/2x2
P2(x) = ln(x)*(x-2)0 + (1/x)*(x-2)1 - (1/2x2)*(x-2)2
P2(x) = ln(x) + 1 - 2/x -1/2 + 2/x - 2/x2
= ln(x) - 2/x2 + 1/2
I'm not very confident in this answer, and don't want to proceed until I figure this out...
I feel like I'm supposed to get an actual number here...
How else would I be able to calculate the max error if I don't have a number?
When it says "centered at 2," that doesn't mean the x is 2, does it? I thought it meant that only the a is 2. Is this right?
Thanks! :)
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