_t +∈fty t^2 + t - t = \_\_\_\_ (Round off to one decimal place)

GATE DA 2025 Q32: Limit of √(t² + t) − t as t → ∞

$\lim_{t \to +\infty} \sqrt{t^2 + t} - t = \_\_\_\_$

(Round off to one decimal place)

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 2025 final answer key)

Concept used: Rationalising an $\infty - \infty$ limit.

First step: Multiply and divide by $\sqrt{t^2 + t} + t$ to get $\dfrac{t}{\sqrt{t^2 + t} + t}$ , then divide the top and bottom by $t$ .

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key