1. BC Calculus
Number 6

3. Memorized Power Series in your Brain….
cos x ex
sin x
ln x

4. General Term

5. and
Use what you just wrote down!
Substitute for cos x

6. General Term
Clean up!

7. Since the First Derivative equals 0 at x=0, x=0 is a critical point, so “neither” is not your answer, but you still have to take another derivative.
Since the Second Derivative is positive at x=0 the graph is concave up, making the critical point at x=0 a minimum.

8. The Fifth Degree Taylor Polynomial for g:

9. Coefficients for the power series

10. Use coefficients from previous slide

11. Series from part (c)! Use the first 3 terms
Plug in 1 for x

12. From the fifth degree polynomial in part (c)
The error in the estimate is less than or equal to the absolute value of the first neglected term!
Plug in a 1 for x
From the fifth degree polynomial in part (c)
this is the first neglected term

13. It's Over!