Checkpoint 3 Answers

1. For every negative `x` the error is bounded by `t^(n+1)text[/]text([)text[(]n+1text[)(]1-t text[)]text(])`, where `t= text[|] x text[|]`. For `x=-1//2`, this bound is `1text[/]text([)2^ntext[(]n+1text[)]text(])`.
2. `-(1/2+1/(2 cdot 2^2)+ 1/(3 cdot 2^3) + 1/(4 cdot 2^4)+cdots)
3. `n=7`
4. `-0.69226`
5. `ln 0.5=-0.69314`
6. The actual error is `0.000885` as opposed to the estimated error of `0.000977`. The error bound is fairly close to the actual error — just over 10% greater than the actual error.