Given the following data points
x_(i)=[-1,-0.8,-0.6,-0.4,-0.2,0,0.2,0.4,0.6,0.8,1]
f_(i)=[14.7781,9.9061,6.6402,4.4511,2.9836,2.0,1.3406,0.8987,0.6024,0.4038,0.2707]
Find the derivative
f^(')(0.4)
using the following methods: a)
1^(st )
order forward difference. b)
2^(nd )
order forward difference. c)
1^(st )
order backward difference. d)
2^(nd )
order backward difference. e)
2^(nd )
order central difference. f)
4^(th )
order central difference. Find
\int_(-1)^1 f(x)dx
using the following methods: a) Trapezoidal Rule b) Simpson's
(1)/(3)
Rule. c) Simpson's
(3)/(8)
Rule (from
x=-1
to
x=0.8
) and Trapezoidal Rule (
x=
0.8 to
x=1
) "Note: Show your detailed work."