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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

If f(θ) = _ n → ∞ ∑_ r=0 ^ nθ 2r n (3θ n - 2r)(nθ + 2r) then :

If f(θ)=lim⁡n→∞∑r=0nθ2rn(3θn−2r)(nθ+2r)f(\theta) = \lim_{n \to \infty} \sum_{r=0}^{n\theta} \frac{2r}{n\sqrt{(3\theta n - 2r)(n\theta + 2r)}} then :

Options

  1. Af(1)=π6f(1) = \frac{\pi}{6}
  2. Bf(\theta) = \int_0^\theta \frac{dx}{\sqrt{\theta^2 - \left( x - \frac{\theta}{2} \right)^2}}
  3. Cf(θ)f(\theta) is a constant function
  4. Dy=f(θ)y = f(\theta) is invertible

Correct answer

A. f(1)=π6f(1) = \frac{\pi}{6}

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