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

Let f:RR be such that f(1) = 3 and f' (1) = 6.Then limx0f(1+x)f(1)1/x equals. 

  1. A

    1

  2. B

    e1/2

  3. C

    e2

  4. D

    e3

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    Solution:

    We have,

    limx0f(1+x)f(1)1/x=limx01+f(1+x)f(1)f(1)1/x=elimx0f(1+x)f(1)xf(1)=e1f(1)limx0f(x+i)f(1)x=ef(1)f(1)=e6/3=e2 limx0f(1+x)f(1)x=f(1)

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