I need to Evaluate at X=.3 and .5 with precision of n=8 and I need to find the maximum error. I am very lost. Thank you.
Ok, first notice that
So
Now notice that a power series is uniformly convergent, thus integrable on its interval of convergence so
Now input the appropriate values and note that if and that
Or in other words the error is less than or equal to the first neglected term. So lets say your error is , then you need to find such that and that will be the correct number of terms. But remember that since if you calcluate the correct to be lets say you really want .