The function f is such that : f(xy)=f(x)...

The function `f` is such that : `f(xy)=f(x)+f(y), x, y gt 0` and `f\'(1)=2` and `A` the area bounded by the curves `y=f(x), x=2` and the x-axis, then (A) `f(x)=2log_ex` (B) `f(x)=2 log_ex` (C) `A=2(2log_e2-1)` (D) `A=4log(2/sqrt(e))`

Similar Questions

Explore conceptually related problems

The area bounded by the curve y=2^(x), the x- axis and the left of y-axis is (A) log _(e)2(B)log_(e)4 (C) log_(4)e(D)log_(2)e

If y=f(x) is the solution of equation ydx+dy=-e^(x)y^(2) dy, f(0)=1 and area bounded by the curve y=f(x), y=e^(x) and x=1 is A, then

If f:R rarr R be a function such that f(x+2y)=f(x)+f(2y)+4xy, AA x,y and f(2) = 4 then, f(1)-f(0) is equal to

If f(x)=log_x(log_ex) then f'(e) =________

Let a function f(x) be such that f"(x)=f'(x)+e^(x)&f(0)=0,f'(0)=1 then find the value of ln(((f(2))^(2))/(4))

Area bounded by the curve f(x)={log_(e)|x|,|x|>=(1)/(e)|x|-1-(1)/(e),|x|<(1)/(2) and x axis is

If f(x) = log_(x^(2)) (log_(e) x) "then f' (x) at x= e" is

Range of the function f(x)=log_(e)sqrt(4-x^(2)) is

f'(x^(2))=(ln x)/(x^(2)) and f(1)=-(1)/(4), then (A)f(e)=0(B)f'(e)=(1)/(20)