You're in Steve Desjardins' class? Aren't you?
So it says find the Maclaurin series of
Then the part I don't get: How many terms of the series are required so that the error of the approximation is at most 0.01 for all x in the interval [−2, 2] ?
I know the Mac. Series is (2x)^n/n! but how to find the error?
If you truncate the MacLaurin series at n - 1 (including the n - 1 term in your approximation), then the error is:
is here some unknown value between 0 and x.
Demanding a maximum error of means that we want:
for ALL values of x and in the area . The expression has a maximum value at . So then we should find the smallest value of n possible for which:
I don't have my calculator for the moment, but I guess you can check for yourself for what n this is true.