# 1. Let f(r) 3, for each positive integer n, consider the regular partition0 ox2 < - *. < In-1 < In = 1of 0, 1] into n many equal-sized subintervals. Denote the corresponding Right-handRiemann sum byΣία) Δi=1(a) For each n, Rnrdx, but what is the smallest value of n for which Rn is withind? (Hint: find a formula for Rn in terms of n)0.1 of the exact value of(b) If a different choice for rin ri-1, X], for i = 1,2, ... , n is chosen to construct theRiemann sumΣ)Δni=1Idr, for a smaller valuecan the resulting sum be within 0.1 of the exact value ofof n than in part (a)? If so, give an example. If not, explain why

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Step 1

The problem concerns estimating errors in calculating the Right hand Riemann sums (to approximate definite integrals)

Step 2

a) Notation following the problem statement

Step 3

a) Determining the right ha...

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