I just want to make sure I'm doing this right.
So we're given the funciton
we're first asked to find the 4th degree taylor polynomial centered at
we're then asked to use taylor's inequality to bound the error in the approximation
well, so i'd want to use ?
if i understand correctly, I want M to be as big as possible. and since this is centered at a=1, this would give me
this just seems like quite a big maximum error to me.
if someone could confirm that this is the error i should be getting, that'd be great.
ah, right. I thought about that when I was posting. I should've taken a bit more time and corrected it. so the upper bound comes from
so I should've had
and out of curiosity how did you get the absolute error? did you use a calculator for the value and then compare it?
it appeared to me that this might actually be able to be broken down into an alternating series so that i then might use the alternating series estimation theorem on it....but i wasn't sure.