PERTEMUAN 9-10 OFC

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PERTEMUAN 9-10
OFC
Soal 1. Consider the function
. Find the formula for the fourth
derivative
, it will be used in our explorations for the remainder term and
the truncation error bound. Graph
. Find the
bound
. Look at it's graph and estimate the value
, be
sure to take the absolute value if necessary.
Soal 2 (a). Compute numerical approximations for the derivatives
, using step sizes
.
(b). Plot the numerical approximation
over the interval
. Compare it with the graph of
over the interval
.
Soal 3 (a). Compute numerical approximations for the derivatives
, using step sizes
.
(b). Plot the numerical approximation
over the interval
Compare it with the graph of
over the interval
.
.
Soal 4. Plot the absolute error
over the interval
, and
estimate the maximum absolute error over the interval.
(a). Compute the error bound
and observe
that
over
.
(b). Since the function f[x] and its derivative is well known, and we have the
graph for
, we can observe that the maximum error on the
given interval occurs at x=0. Thus we can do better that "theory", we see that
over
.
Soal 5. Investigate the behavior of
then the error bound is reduced by
. If the step size is reduced by a factor of
. This is the
Terima kasih
behavior.
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