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GATE 2023 MT – Question 23

Engineering Mathematics · Calculus and vector calculus · 1 mark · Multiple choice

The value of $\displaystyle\lim_{x\to1}\frac{7x^7-20x^5+13x}{3x^3+x-4}$ is

  1. $-38/10$
  2. $-51/10$
  3. $38/10$
  4. undefined

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Correct answer: (A) $-38/10$

Explanation

Both numerator and denominator vanish at 1. L’Hôpital gives numerator derivative $49x^6-100x^4+13$, equal to −38 at 1, and denominator derivative $9x^2+1$, equal to 10. The limit is $-38/10$, **A**.