to some degree -- for example, start with a degree 5
approximation.
Evaluate the error term for this approximation by recalling from
calculus that the Taylor series error for the 
degree
Taylor polynomial of a function g on the interval [a - r, a + r]
is given by 
where t ranges over the interval [a - r, a +
r]. Use
Maple's graphical abilities to help you obtain an upper bound for the
error term. How small does the error term have to be in order for the
integral of the Taylor approximation to to agree with
In doing this problem you should be familiar with the Maple commands
taylor and convert( , polynom). As well, you should
recall that in order to evaluate the order
derivative of a function g it is possible to use the command
D@@n(g). In some cases, such as calculating a large iterated
derivative, you may find it convenient to suppress the output of the
calculation because it scrolls on for several screens. Remember
that this can be done by ending the command with a colon instead of a
semicolon.
