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 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).

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x),x 0} Find g(x) such that f(x) is continuous and f'(1)=f(-1)

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)=

If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

Two functions f&g have first &second derivatives at x=0 & satisfy the relations,' f(0)=2/(g(0)),f'(0)=2g'(0)=4g(0),g

If f and g are derivable function of x such that g'(a)ne0,g(a)=b" and "f(g(x))=x," then 'f'(b)=

Let f and g be differentiable on R and suppose f(0)=g(0) and f'(x) =0. Then show that f(x) =0