Find an approximated value for using a Taylors polynomial of third degree and estimate the error.
I thought of solving it by using
Then I evaluated it at x=9.03, so I get:
I don't know if this is right, I've tried with the calculator and it gives 3.00500.... Now, how do I estimate the error? just by resting to the value the calculator gives the one I get?
correct the cubic term ...
since the series is alternating, the error will be less than the first omitted term ...
Should it not be 0.03 in your brackets rather than 0.3?
Regardless, the error of an nth order Taylor Polynomial using a stepsize of h is always of the order of
So, in your case, I would estimate the error to be of the order of
Thanks. Skeeter, how did you get the expression?
I think you're using the expression for the residual, that looks quiet similar to the expressions of the terms for the Taylors polynomial.
The thing is that the reminder is:
where is such
mmm I think I'm getting it, so ?
And then thats why the error is smaller than the expression for the reminder. Right? thank you very much Skeeter.
no need for computing an error bound ... for a strictly alternating series, the error is no greater than the first omitted term. In this case ...