Estimation of Taylor series

http://i.imgur.com/5Dj9g4P.jpg

For question 11 (which I think is more straightforward than 10), I think I have the answer, which is 2decimal places

For question 10, I end up with the following formula

R9 = (Cos(w) (2-pi/2) ^{9} )/9!

However, I have never understood what w is (some textbooks and videos use z) other than it is a number between x and c. I assume x is 2 and c is pi/2 but what number is inbetween. Depending on what I use I get a massive difference in "error". What is w?

Re: Estimation of Taylor series

Hey lukasaurus.

The statement is that w is a number between x and c and is just an existence theorem: in other words, the proof says that the condition exists and not what it is.

What you should do is to use the statement to get the maximum possible error and use that to get the answer for the sine.