1 Use The Peano Kernel To Determine The Error Of The Trapezoidal Sum Rule 2 Calculat 1896333

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1. Use the Peano kernel to determine the error of the trapezoidal sum rule.

2. Calculate the numerical convergence of (9.39) and (9.40) with the composite trapezoidal sum rule to show that the possession of derivatives does matter.

3. Show that Romberg integration with two levels of resolution h0 and h1 = h0/2 gives Simpson's rule, and with three levels of resolution (h2 = h0/4) gives Boole's rule.