Let f: R R be such that f(1)=3 and f^ (1)=6 . Then _ x 0 ( f(1+x) f(1) )^ 1 / x equals

Mathematics · JEE Main · NTA ExamsLimit, Continuity and Differentiability

Let \(f: R \rightarrow R\) be such that \(f(1)=3\) and \(f^{\prime}(1)=6 \text {. Then } \lim _{x \rightarrow 0}\left(\frac{f(1+x)}{f(1)}\right)^{1 / x}\) equals  
  1. \(1\)
  2. \(e^{1 / 2}\)
  3. \(e^{2}\)
  4. \(e^{3}\)

Answer

(C) e^ 2

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