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AIEEE 2002

JEE Main 2002 Mathematics question on Limits Continuity and Differentiability

Let f:R→Rf: R \to R be such that f(1)=3f(1) = 3 and f′(1)=6f'(1) = 6. Then, lim⁡x→0[f(1+x)f(1)]1/x\lim_{x \to 0} \left[\frac{f(1+x)}{f(1)}\right]^{1/x} equals
  1. A.
    11
  2. B.
    e1/2e^{1/2}
  3. C.
    e2e^2
  4. D.
    e3e^3
Show answer

Correct option: C

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