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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

Evaluate _ n → ∞ ( (1^2)/(n^3+1^3) + (2^2)/(n^3+2^3) +...

Evaluate lim⁡n→∞\lim_{n \to \infty} (12n3+13+22n3+23+32n3+33+…⋯+49n)\left( \frac{1^2}{n^3+1^3} + \frac{2^2}{n^3+2^3} + \frac{3^2}{n^3+3^3} + \dots \dots + \frac{4}{9n} \right)

Options

  1. A13ln⁡3\frac{1}{3} \ln 3
  2. Bln⁡93\frac{\ln 9}{3}
  3. Cln⁡43\frac{\ln 4}{3}
  4. Dln⁡63\frac{\ln 6}{3}

Correct answer

A. 13ln⁡3\frac{1}{3} \ln 3

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