Let f x cos x Approximate the integral I f z dz in three different ways each with n 4 a a Right Riemann Sum b the Trapezoidal

Question

Let f x cos x Approximate the integral I f z dz in three different ways each with n 4 a a Right Riemann Sum b the Trapezoidal Rule and c Simpson s Rule Give each answer correct to six decimal places a R b T c S4 It can be shown that for each z in 0 1 z 4 and f z 43 Combine these facts with the error control inequalities discussed in class to complete the following guarantees concerning the absolute errors in the approximations from parts b a Give each answer correct to six decimal places d I Tel e I Sal Using the facts given for parts d and e and the error formulas find the smallest integer n for which we can guarantee that the approximation T is within 107 of the exact value a Repeat for S 1 For T n g For S n Which wo su rath

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