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If `f(x)` is a monic polynomial of degree `'3'` such that `lim_(x to 0) (1+f(x))^(1/(x^(2)))=e^(-3), g(x)=(f(x))/(x^(3))dx` and `g(1)=1` then On the basis of above information, answer the following question: Value of `g(e)` is

A

`e-3`

B

`3-e`

C

`3`

D

`e+3`

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