Really - Taylor Polynomial Approximation Error

[bcjochim07]

Homework Statement

Use Taylor's theorem to obtain an upper bound of the error of the approximation. Then calculate the exact value of the error.

cos(.3) is approximately equal to 1 - (.3)^2/2! + (.3)^4/4!

Homework Equations

The Attempt at a Solution

I came up with upper bound saying

Rn = (-sinz/5!)*(.3)^5 < (.3)^5/5!

so the upper bound is (.3)^5/5! which is about .00002

But for the exact error I have no idea how to calculate it. There aren't any examples in my textbook.

 

[Vid]

I think they want you to use a calculator to actually find cos(.3) then subtract the approximation to see if how well your estimate worked.

 

[Dick]

The only way to calculate the exact value of the error is to take the exact value of the cosine and subtract the value of the series. I think they just mean punch cos(.3) into your calculator and then subtract the series value and see that it's less than the remainder term.