In the refnement of the approximation it is a good idea to consider ܰ-
values of the form 2 ,i.e. powers of 2, since you can then reuse the already calculated
values from the previous iteration round.
(1) Compute the approximation of Store the
results in a list. Print the result of the individual calculations as well as the deviations
from the exact value.
(2) What assumption about convergence speed can be deducted?
(3) Check your assumption for the integral
In the last two exercises, the integral could be calculated directly by considering the
antiderivative. Of course, numerical integration is of particular interest if the integral
cannot be expressed in a closed representation by known antiderivatives.