What is the maximum possible error generated in using the 5th degree Maclaurin polynomial for sin(x) for x in the interval [−0.3, 0.3]?

Question

What is the maximum possible error generated in using the 5th degree Maclaurin polynomial for sin(x) for x in the interval [−0.3, 0.3]?

A
B
C	The value cannot be determined.
D	There is no error. The value will be exact.

Answer 1

The error is approximately .3^7/7!

You can get the exact answer by calculating |sin(.3) - the MacLaurin approximation|

I you calculate |sin(.3) - .3 + .3^3/3!-.3^5/5!|, you will see that it is very close to .3^7/7!