Latihan 2

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Latihan 2
Soal 1 (a). Compute numerical approximations for the derivative
, using step
sizes
, include the details.
(b). Compute numerical approximations for the derivatives
, using step sizes
.
(c). Plot the numerical approximation
over the interval
.
Compare it with the graph of
over the interval
.
Soal 2. 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 3. Investigate the behavior of
then the error bound is reduced by
. If the step size is reduced by a factor of
. This is the
behavior.
Soal 4 Given
derivative
, find numerical approximations to the
, using two points and the forward difference formula.
Soal 5 Given
derivative
, find numerical approximations to the
, using two points and the forward difference formula.
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