Part BCSIR NET December 2024the-rate-of-a-riemann-sum-not-just-its-limit

The rate of a riemann sum not just its limit

Let $f : [0, 1] \to R$ be defined by $f (x) = sin (x^{2})$ . Let $A = lim (n \to \infty) (\sum_{(} k = 1)^{n} f (k / n) - n \int_{0}^{1} f (x)$ dx). Which of the following statements is true?

A.A = 0
B.A = 1
C.A = sin(1)/2✓
D.A = sin(1/4)

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: |f| Riemann integrable ⇒ f Riemann integrable

The rate of a riemann sum not just its limit

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