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GATE 2020 CE (CE1) – Question 12

Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 1 mark · Multiple choice

Evaluate $\lim_{x\to\infty}(x^2-5x+4)/(4x^2+2x)$.

  1. 0
  2. 1/4
  3. 1/2
  4. 1

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Correct answer: (B) 1/4

Explanation

Divide numerator and denominator by $x^2$. Terms involving $1/x$ and $1/x^2$ vanish as x tends to infinity. The limit is the leading-coefficient ratio **1/4, B**.