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GATE 2020 ME (ME1) – Question 12

Engineering Mathematics · Calculus: Limit, continuity, differentiability, mean value theorems and indeterminate forms · 1 mark · Multiple choice

Evaluate $\displaystyle\lim_{x\to1}\frac{1-e^{-c(1-x)}}{1-xe^{-c(1-x)}}$.

  1. $c$
  2. $c+1$
  3. $c/(c+1)$
  4. $(c+1)/c$

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Show answer and explanation

Correct answer: (C) $c/(c+1)$

Explanation

Both numerator and denominator vanish at x=1. Their derivatives are $-ce^{-c(1-x)}$ and $-(1+cx)e^{-c(1-x)}$. L’Hôpital’s rule gives **c/(c+1), C**, where c≠−1. The common exponential cancels.