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Part CCSIR NET December 2024two-conditions-determine-the-pair

Two conditions determine the pair

If λ∈R\lambda \in \mathbb{R} and p∈Rp \in \mathbb{R} are such that the quadrature formula ∫(x0)(x0+h)f(x)\int_(x_{0})^(x_{0}+h) f(x)dx ≈λh(f(x0)+f(x0+h))+\approx \lambda{}h(f(x_{0}) + f(x_{0} + h)) + ph3(f′′(x0)+f′′(x0+h))^{3}(f''(x_{0}) + f''(x_{0} + h)) is exact for all polynomials of degree as high as possible, then

  1. A.2λ+24p=02\lambda + 24p = 0✓ Correct
  2. B.7λ−12p=47\lambda - 12p = 4✓ Correct
  3. C.2λ+24p=−32\lambda + 24p = -3
  4. D.7λ−12p=117\lambda - 12p = 11

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, and why this one tests numerical convergence.

See pricing

50 are analysed free — try those first.

The trap it tests

Numerical convergence

A scheme assumed to converge, or to converge at its advertised rate.

Drill statements like this

Related counterexample: Increasing the number of equally spaced interpolation nodes improves the approximation

More on this topic

The chapter behind this: Interpolation and numerical integration — free to read

From Numerical Analysis › Interpolation and numerical integration with error terms

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