Let `f^(prime)(x)=e^x^2 and f(0)=10.` If `A`

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

Let the function f satisfies f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) foe all x and f(0)=3 The value of f(x).f^(prime)(-x)=f(-x).f^(prime)(x) for all x, is

Suppose f is a differentiable real function such that f(x)+f^(prime)(x)lt=1 for all x , and f(0)=0, then the largest possible value of f(1) is (1) e^(-2) (2) e^(-1) (3) 1-e^(-1) (4) 1-e^(-2)

Let f(x y)=f(x)f(y)\ AA\ x ,\ y in R and f is differentiable at x=1 such that f^(prime)(1)=1 also f(1)!=0 , f(2)=3 , then find f^(prime)(2) .

If f: RvecR is a differentiable function such that f^(prime)(x)>2f(x)fora l lxRa n df(0)=1,t h e n : f(x) is decreasing in (0,oo) f^(prime)(x) e^(2x)in(0,oo)

Let y=f(x) is a solution of differential equation e^(y)((dy)/(dx)-1)=e^(x) and f(0)=0 then f(1) is equal to

Let f(x)=e^(x)g(x),g(0)=4 and g'(0)=2, then f'(0) equals

Suppose f,f' and f" are continuous on [0,e] and that f^(prime)(e)=f(e)=f(1)=1 and int_1^e(f(x))/(x^2)dx=1/2, then the value of int_1^0 f*(x)ln xdx equals.