Let `f(x)=x sin pix`, `x gt 0` Then for all natural numbers n, f`(x) vanishes at

Let f(x)=x sin pi x,x>0 Then for all natural numbers n,f(x) vanishes at

Let f(x)=sin x,x =0 then

If f(x+y)=f(x)f(y) and sum_(x=1)^(oo)f(x)=2,x,y in N , where N is the set of all natural numbers , then the value of (f(4))/(f(2)) is :

Let f (x) = |sin x| then f (x) is

Let f(x)=(sin x)/(x), x ne 0 . Then f(x) can be continous at x=0, if

Let f(x)= sin((pi)/x) and D={x:f(x)gt0) , then D contains

Let f'(x) gt0 and g'(x) lt 0 " for all " x in R Then

Let f(x)=[n+p sin x],x in(0,pi),n in Z,p a prime number and [x]= the greatest integer less than or equal to x.The number of points at which f(x) is not not differentiable is: