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Newton's interpolating

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Use Newton's interpolating polynomial to approximate the function:

f (x) = e^ (-ax2) a = 1.1125

Construct approximation using the values f (x) at x= -2, -1, 0, 1, 2. Call this approximation N(x).

ii) Compute the value of the integral

accurate to 1 decimal place.

iii) Compute sufficient trapezium rule and the mid-point rule estimates for the integral

So that you may quote the integral's value to 1 decimal place. Hence compute the corresponding Simpson's rule estimate.

Is N(x) a good approximation to f(x)? Give a reason.


Solution Summary

This has various problems regarding Newton's interpolating polynomial and Simpson's rule.