If (x) = mx +c and if f(0)=f'(0)=1, what is f(2) ?

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then The value of underset(x to -oo)(lim)f(x) is

If f(x) = 2x - 5, then f (0) is :

Find a quadratic function defined by the equation: f(x) = ax^2 + bx + c if f(0) = f(-1) = 0 and f(1)=2

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuous differentiable function with f'(x) !=0 and satisfies f(0)=1 and f'(0)=2 , then f(x)=e^(lambda x)+k , then lambda+k is equal to ..........

If f'(x) = a sin x + b cos x and f'(0) = 4,f(0) = 3, f((pi)/(2))= 5 , find f(x).

Find a quadratic function defined by the equation: f(x) = ax^2 + bx + c if f(1) =0,f(2)=-2and f(3)=-6

Let f be a continuous function satisfying f '(l n x)=[1 for 0 1 and f (0) = 0 then f(x) can be defined as (a) f(x)={(1 , "if"x le 0 ),(1-e^(x), "if" x gt 0 ):} " " (b) f(x)={(1,"if" x le 0 ),(e^(x)-1,"if" x gt 0):} (c) f(x)={(x,"if" x lt 0),(e^(x),"if" x gt 0 ):} " " (d) f(x)={(x,"if" x le 0 ),(e^(x)-1,"if" x gt 0):}

if f'(x) = 3x^2-2/x^3 and f(1)=0 , find f(x).

Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y . If f'(0) exits and equals -1 and f(0) =1 , then find f(2) .

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.