GATE 2023 AG – Question 12

Engineering Mathematics · Calculus · 1 mark · Multiple choice

Find $\lim_{x\to0}(\sqrt{1+x}-1)/x$.

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Correct answer: (B) 1/2

Explanation

Rationalize the numerator to obtain $(\sqrt{1+x}-1)/x=1/(\sqrt{1+x}+1)$ for nonzero x near0. Its limit is 1/(1+1)=**1/2,B**. Rationalization removes the apparent0/0 indeterminacy.

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