Use a taylor polynomial to approximate at x=0.1 with error less than 0.001.
The n-th derivative of f is . If you develop f around you get
Where . To make the error term for smaller than 0.001, we solve the following (worst case) inequality for n
which gives, if I'm not mistaken, that . Thus we take and get:
. Compare this with the exact value of : the resulting error is less than 0.001, as required.