Let `f:R to R` be a differentiable function with `f(0)=0`. If `y=f(x)` satisfies the differential equation
`(dy)/(dx)=(2+5y)(5y-2)`, then the value of `lim_(x to oo)f(x)` is……………….

Let f:R rarr R be a differentiable function with f(0)=0. If y=f(x) satisfies the differential equation (dy)/(dx)=(2+5y)(5y-2), then the value of (lim)_(x rarr oo)f(x) is

Let f: R rarr R be a differentiable function with f(0)=0. If y=f(x) satisfies the differential equation dy/dx=(2+5y)(5y-2), then the value of lim_(x rarr - infty) f (x) is …....

A function y=f(x) satisfies the differential equation (dy)/(dx)+x^(2)y+2x=0,f(1)=1 then the value of f(1) is-

If y=f(x) satisfy differential equation ( dy )/(dx)-y=e^(x) with f(0)=1 then value of f'(0) is

Let f:R rarr R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f'(y)+f'(x)f(y) for all x,y in R. Then,the value of (log)_(e)(f(4)) is

Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______