Evaluate the following limit: _x 0 ≤ft((x^2 + 1) x)/x^2 The value of the limit is ______.

GATE DA 2024 Q60: Limit of ln((x²+1) cos x) / x² as x → 0

Evaluate the following limit:

$\lim_{x \to 0} \frac{\ln\left((x^2 + 1)\cos x\right)}{x^2}$

The value of the limit is ______.

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 0.5 (official GATE 2024 final answer key)

Concept used: Limits using series expansions: $\ln(1+u) \approx u$ and $\cos x \approx 1 - \tfrac{x^2}{2}$ near 0.

First step: Split the log: $\ln(1 + x^2) + \ln \cos x \approx x^2 - \tfrac{x^2}{2}$ .

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key