Taylor Polynomial Homework: Estimating x Range with Error < 0.01

[vigintitres]

Homework Statement

I can either use the alternating series estimation thereom (which i don't really know) or Taylor's Inequality to estimate the range of values of x for which the given approximation is accurate to within the stated error.

sin(x) = x - (x^3)/6 (|error| < 0.01)

Do I just start writing out the terms of the sine series? I'm not sure exactly what I'm supposed to do here.

 

[Dick]

You are supposed to estimate the error in a truncation of the infinite series. As you don't seem to know either the alternating series estimate or the Taylor series remainder term, I think you will need to look at least one of them up. Can you do that? I would suggest starting with the alternating series version. It's easier.

 

[vigintitres]

thanks, Dick, I will look that up