Let `f` and `g` be real valued functions defined on interval `(-1,\ 1)` such that `g"(x)` is continuous, `g(0)!=0` , `g'(0)=0,` `g"(0)!=0` , and `f(x)=g(x)sinx` . Statement-1 : `("Lim")_(x->0)[g(x)cotx-g(0)"c o s e c"x]=f"(0)` and Statement-2 : `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 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 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 underset(xrarr0)lim(g(x)cotx-g(0)cosecx)=f''(0) Statement II f'(0)=g'(0)

Let f and g be real valued functions defined on interval (-1, 1) such that g'' (x) is continuous, g(0) ne 0, g'(0) = 0, g''(0) ne 0, and f(x) = g''(0) ne 0 , and f(x) g(x) sin x . Statement I lim_( x to 0) [g(x) cos x - g(0)] [cosec x] = f''(0) . and Statement II f'(0) = g(0).

Find f0g and g0f : f(x) = 2x , g(x)=sinx

Statement I if f(0)=a,f'(0)=b,g(0)=0,(fog)'(0)=c then g'(0)=(c)/(b). Statement II (f(g(x))'=f'(g(x)).g'(x), for all n

Statement I if f(0)=a,f'(0)=b,g(0)=0,(fog)'(0)=c then g'(0)=(c)/(b). Statement II (f(g(x))'=f'(g(x)).g'(x), for all n

Statement I if f(0)=a,f'(0)=b,g(0)=0,(fog)'(0)=c then g'(0)=(c)/(b). Statement II (f(g(x))'=f'(g(x)).g'(x), for all n

If for a continuous function f,f(0)=f(1)=0,f'(1)=2 and g(x)=f(e^(x))e^(f(x)) then g'(0)=