1. AP Calculus BC
2011 Extended Response #6

3. Use the memorized power series for sin(x)
For sin(x2), replace all of the x’s with (x2)’s

5. + Use the memorized power series for cos(x)
Add the two polynomials, combining like terms as necessary

7. If we take 6 derivatives of f, we will be left only with the 6th derivative of the 6th degree of the power series, because all previous terms will no longer exist, and all proceeding terms will come out to 0.
The 6th degree power series is:
Take 6 derivatives
-121

9. = Error
So the first neglected term multiplied by the error maximizing value, f ’(z) must be less than
On the interval from 0 to .25, the maximum possible error is less than 40
Now plug in 40 for f(5)(z) and .25 for x