Find a value for n such that the absolute error in the approximation is less than , given that about 0.
(Note: f(x) = cos(x))
I replace sin(c) with 1, since it is an upper bound, and x with 2:
We want this error to be less that , so:
This is equivalent to finding:
Why?! Of course that then you get what you get since the LHS is the power of a number greater than 2, whereas the RHS
is a negative power of a number greater than 1...! You forgot, or for some reason you
thought, that you can dismiss the LHS's denominator:
So I get .
This isn't right. The answer should be n = 14. Where have I gone wrong? Thanks.