If `f(0)=0=g(0)and f'(0)=6=g'(0)then lim_(xrarr0)f(x)/g(x)=`

f(0)=0=g(0) and f'(0)=6=g'(0)thenlim_(x rarr0)(f(x))/(g(x))=

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuously differentiable function with f'(x)ne0 and satisfies f(0) = 1 and f'(0) = 2 then lim_(xrarr0) (f(x)-1)/(x) is

If f and g are differentiable at a in R such that f(a)=g(a)=0 and g'(a)!=0 then show that lim_(x rarr a)(f(x))/(g(x))=(f'(a))/(g'(a))

Let fandg be real valued functions defined on interval (-1,1) such that g''(x) is constinous, g(0)=0 , g'(0)=0,g''(0)=0andf(x)=g(x)sinx . Statement I lim_(xrarr0)(g(x)cotx-g(0)cosecx)=f''(0) Statement II f'(0)=g'(0)

Let fandg be real valued functions defined on interval (-1,1) such that g''(x) is constinous, g(0)=0 , g'(0)=0,g''(0)=0andf(x)=g(x)sinx . Statement I lim_(xrarr0)(g(x)cotx-g(0)cosecx)=f''(0) Statement II f'(0)=g'(0)

Let f:R rarr R be differentiable at x = 0. If f(0) = 0 and f'(0)=2 , then the value of lim_(xrarr0)(1)/(x)[f(x)+f(2x)+f(3x)+….+f(2015x)] is

Let f:RrarrR be differentiable at x=0 . If f(0)=0 and f'(0)=2 ,then the value of lim_(xrarr0)1/x[f(x)+f(2x)+f(3x)+.....+f(2015x)] is

Let fandg be real valued functions defined on interval (-1,1) such that g''(x) is constinous, g(0)!=0 , g'(0)=0,g''(0)!=0andf(x)=g(x)sinx . Statement I lim_(xrarr0)(g(x)cotx-g(0)cosecx)=f''(0) Statement II f'(0)=g(0)

If g(x) = (x^(2)+2x+3) f(x) and f(0) = 5 and lim_(x rarr 0) (f(x)-5)/(x) = 4, then g'(0) =