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GATE 2014 EC (EC2) – Question 14

Engineering Mathematics · Calculus · 1 mark · Multiple choice

Evaluate $\lim_{x\to\infty}(1+1/x)^x$.

  1. $\ln2$
  2. 1.0
  3. $e$
  4. $\infty$

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Show answer and explanation

Correct answer: (C) $e$

Explanation

Take logarithms:L=lim xln(1+1/x). With u=1/x→0, this becomes lim ln(1+u)/u=1. Exponentiating gives the original limit **e,C**. The base approaches1 while the exponent grows, so direct substitution is indeterminate.