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GATE 2024 BT – Question 63

Engineering Mathematics · Calculus: Limits, continuity, differentiability, partial derivatives, maxima and minima · 2 marks · Numerical answer

The value of the limit $\lim_{x\to\infty}\frac{x}{2}\ln\left(1 + \frac{2024}{x}\right)$ is ________.

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Correct answer: 1012

Explanation

Put $u = \frac{1}{x}$: $\frac{1}{2}\cdot\frac{\ln(1 + 2024u)}{u} \to \frac{1}{2}\times 2024 = 1012$.