`f'(3) +f'(2) = 0` Find the `lim_(x rarr 0) ((1+f(3+x)-f(3))/(1+f(2-x)-f(2)))^((1)/(x))`

f'(3)+f'(2)=0 Find the lim_(x rarr0)((1+f(3+x)-f(3))/(1+f(2-x)-f(2)))^((1)/(x))

f(x)=e^x then lim_(x rarr 0) f(f(x))^(1/{f(x)} is

If f'(x)=f(x) and f(0)=1 then lim_(x rarr0)(f(x)-1)/(x)=

If f'(2)=4 then,evaluate lim_(x rarr0)(f(1+cos x)-f(2))/(tan^(2)x)

If f(1)=3 and f'(1)=6 , then lim_(x rarr0)(sqrt(1-x)))/(f(1))

If f'(2)=6 and f'(1)=4 ,then lim_(x rarr0)(f(x^(2)+2x+2)-f(2))/(f(1+x-x^(2))-f(1)) is equal to ?

If f(x) is twice differentiable and f^('')(0) = 3 , then lim_(x rarr 0) (2f(x)-3f(2x)+f(4x))/x^(2) is

If f'(0)=3 then lim_(x rarr0)(x^(2))/(f(x^(2))-6f(4x^(2))+5f(7x^(2))=)

Let R rarr R be such that f(1)=3 and *f'(1)=6. then lim_(x rarr0)((f(1+x))/(f(1))) equal : (1)1(2)e^((1)/(2))(3)e^(2) (4) e^(3)