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GATE 2016 ME (ME3) – Question 38

Engineering Mathematics · Calculus: Limit, continuity, differentiability, mean value theorems and indeterminate forms · 2 marks · Multiple choice

The limit $\lim_{x\to\infty}(\sqrt{x^2+x-1}-x)$ is ______.

  1. 0
  2. $\infty$
  3. 1/2
  4. $-\infty$

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Correct answer: (C) 1/2

Explanation

Rationalise √(x²+x−1)−x to obtain(x−1)/(√(x²+x−1)+x). Dividing numerator and denominator by positive x gives(1−1/x)/(√(1+1/x−1/x²)+1). The limit is **1/2, C**. Direct subtraction of two unbounded terms is indeterminate.