GATE 2025 DA – Question 32
$\lim_{t \to +\infty}\sqrt{t^2 + t} - t = $ ______ (*Round off to one decimal place*)
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Correct answer: 0.49 to 0.51
Explanation
Multiply by the conjugate: $\sqrt{t^2 + t} - t = \frac{t}{\sqrt{t^2 + t} + t} = \frac{1}{\sqrt{1 + 1/t} + 1}$. As $t \to \infty$ this tends to $\frac{1}{1 + 1} = 0.5$.