GATE 2015 CS (CS3) – Question 24
Evaluate $\lim_{x\to\infty}(1+x^2)^{e^{-x}}$.
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Correct answer: (C) 1
Explanation
Take logarithms: log of the expression is e⁻ˣ log(1+x²), which tends to zero because exponential decay dominates logarithmic growth. Exponentiating yields e⁰=1. Thus C; the form ∞⁰ must be evaluated rather than treated as a literal power.