In this problem, you will investigate the error in the
degree Taylor approximation, , to
about for various values of .
(a)
Let . Using a calculator or
computer, graph for , and notice
what shape the graph is. Then use the Error Bound for Taylor polynomials
to find a formula for the maximum error, as a function of ,
in this case:
.
Graph the actual error and your error bound together to
see that the error is in fact below the maximum error bound (but close
to it).
(b)
Let . Choose a suitable range
and graph for . Again, notice what
shape the graph of is. Then use the Error Bound for Taylor
polynomials to find a formula for the maximum error, as a function
of , in this case:
.
Graph the actual error and your error bound together to
see that the error is in fact below the maximum error bound (but close
to it).
You can earn partial credit on this problem.