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If f(x) be a differentiable function fo...

If `f(x)` be a differentiable function for all positive numbers such that `f(x.y) = f(x) +f(y) and f(e) = 1` then `lim_(x->0) (f(x+1))/(2x)`

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Knowledge Check

  • Let f (x) is a differentiable function such that f (x + y) = f (x) + f (y) + 2xyAAx, y in R and lim_(x to 0) (f(x))/(x) = 210 , then f (2) is equal

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  • A differentiable function f (x) satisfies the condition f(x+y) =f(x) + f(y) + xy and lim_(h to 0) 1/h f(h) = 3 then f is:

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    linear
    B
    `f(x) =3x + x^(2)/2`
    C
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  • Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + ff(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

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