# Really need help - Taylor Polynomial Approximation Error

1. 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!

2. Homework Equations

3. 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.

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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