[考古] 清大86

[johnnyzsefb (AJ)]

 II.
 　　
　2.(14%) If f:R→R satisfies f(x+y)=f(x)f(y) for all x,y belong to R and

         f(x)=1+xg(x) where lim g(x)=1.
                            x→0
         Show that f is differentiable,and find f(x).

         以上

              感謝~XD

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推 axis0801:提示:利用導函數的定義,可證出f'(x)=f(x)
→ axis0801:利用變數分離解f'(x)=f(x)找出f(x)的通式