Checkpoint 5

1. Explain the simplification `a_(k+1)/a_k=(text[(]2k+1text[)]! |x|^(2k+3))/ (text[(]2k+3text[)]! |x|^(2k+1))=|x|^2/(text[(]2k+3text[)(]2k+2text[)]).
2. Calculate the error estimate `a_n=1/(text[(]2n+1text[)]!) |x|^(2n+1)` for `x=5` and `n=7`.
3. Calculate the sum of the first 7 terms of the series for `sin x` with `x=5`.
4. Compare the sum in part (c) with your computer's or calculator's approximation to `sin 5`. How close is the estimate in part (b) to the actual error?