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GATE 2021 CE (CE2) – Question 11

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

Find $\lim_{x\to\infty}x\ln x/(1+x^2)$.

  1. 0
  2. 1.0
  3. 0.5
  4. $\infty$

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Show answer and explanation

Correct answer: (A) 0

Explanation

Divide numerator and denominator by x² to get $(\ln x/x)/(1+1/x^2)$. The numerator tends to zero because logarithmic growth is slower than linear growth, and the denominator tends to one. Therefore the limit is **0 (A)**.