Evaluate x0[(1-x)n-1]/x.

GATE 2022 MN – Question 11

Engineering Mathematics · Calculus · 1 mark · Multiple choice

Evaluate $\lim_{x\to0}[(1-x)^n-1]/x$.

0
1
$-n$
$n$

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Show answer and explanation

Correct answer: (C) $-n$

Explanation

This is the derivative of (1−x)^n at x=0. Differentiating gives −n(1−x)^(n−1), whose value at zero is −n. Hence C. Equivalently, the first-order expansion is (1−x)^n=1−nx+O(x²).

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