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GATE 2017 CS – Question 38

Engineering Mathematics · Calculus · 2 marks · Multiple choice

The value of $\lim_{x \to 1} \dfrac{x^7 - 2x^5 + 1}{x^3 - 3x^2 + 2}$

  1. is 0
  2. is $-1$
  3. is 1
  4. does not exist

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Correct answer: (C) is 1

Explanation

At $x = 1$ both the numerator ($1 - 2 + 1$) and the denominator ($1 - 3 + 2$) are 0, so apply L'Hopital's rule. The derivatives are $7x^6 - 10x^4$ and $3x^2 - 6x$, which at $x = 1$ give $-3$ and $-3$. The limit is $\frac{-3}{-3} = 1$.