`f'(3) +f'(2) = 0` Find the `underset(x rarr 0)lim((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) is the function such that underset( x rarr 0 ) ("Lim") (f(x))/( x ) = 1 . If underset( x rarr 0 ) ( "Lim") ( x ( 1+ a cos x )-b sinx ) /( (f(x))^(3))= 1 , then find the value of a and b.

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

If f(x) is a polynomial of least degree,such that lim_(x rarr0)(1+(f(x)+x^(2))/(x^(2)))^((1)/(x))=e^(2), then f(2) is

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

If f'(x)=k,k!=0, then the value of lim_(x rarr0)(2f(x)-3f(2x)+f(4x))/(x^(2)) is

Let f'(x) be continuous at x=0 and f'(0)=4 then value of lim_(x rarr0)(2f(x)-3f(2x)+f(4x))/(x^(2))

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