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 Exams — Limit, 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
- \(1\)
- \(e^{1 / 2}\)
- \(e^{2}\)
- \(e^{3}\)
Answer
(C) e^ 2
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