Let `f:RrarrR` be such that `f(a)=1, f(a)=2`. Then `underset(xrarr0)(lim)((f^(2)(a+x))/(f(a)))^(1//x)` is

Let f:RrarrR be such that f(a)=1, f(a)=2 . Then lim_(x to 0)((f^(2)(a+x))/(f(a)))^(1//x) is

If f(a) = 2, f'(a) = 1, g(a) = -1, g' (a) = 2 . Then underset(x rarr a)(lim) (g (x) f(a) - g(a) f(x))/(x -a) is

If f(1)=1 and f'(1)=2 then lim_(xto1)((f(x))^(2)-1)/(x^(2)-1) is

Let f: RrarrR, where f(x)=sinx , Show that f is into.

Let f(x) be the fourth degree polynomial such that f^(prime)(0)=-6,f(0)=2 and (lim)_(x->1)(f(x))/((x-1)^2)=1 The value of f(2) is a. 3 b. 1 c. 0 d. 2

Let f(x)=2x+5 . If xne0 then find (f(x+2)-f(2))/(x)

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 f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

Let f :RtoR be a positive, increasing function with lim_(xtooo) (f(3x))/(f(x))=1 . Then lim_(xtooo) (f(2x))/(f(x)) is equal to

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to