If `f^(prime)(x)=g(x)(x-a)^2,w h e r eg(a)!=0,a n dg` is continuous at `x=a ,` then (a) `f` is increasing in the neighbourhood of `a` if `g(a)>0` (b)`f` is increasing in the neighbourhood of `a` if `g(a)<0` (c)`f` is decreasing in the neighbourhood of `a` if `g(a)>0` (d)`f` is decreasing in the neighbourhood of `a` if `g(a)<0`

If f.g is continuous at x = 0 , then f and g are separately continuous at x = 0 .

If f.g is continuous at x = 0 , then f and g are separately continuous at x = 0 .

Given that f(x) = xg (x)//|x| g(0) = g'(0)=0 and f(x) is continuous at x=0 then the value of f'(0)

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

If f"(x)>0AAx in R, f'(3)=0,and g(x)=f("tan"hat2x-2"tan"x+4),0

If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in this interval

If f(x)=sgn(x)={(|x|)/x,x!=0, 0, x=0 and g(x)=f(f(x)), then at x=0,g(x) is

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

If g(x) is a decreasing function on R and f(x)=tan^(-1){g(x)} . State whether f(x) is increasing or decreasing on R .

If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v) is