If `f(x) = sin (1/x)`, then at `x=0`

If f(x)=x sin ((1)/(x)),x ne 0 then the value of the function at x=0, so that the function is continuous at x=0 is

If f(x)=x sin(1/x), x!=0 then (lim)_(x->0)f(x)=

Let the function f be defined by f(x) = "x sin" (1)/(x) , when x ne 0 = 0 , when x = 0. Then at x = 0, f is :

Show that the function f(x)={x sin((1)/(x)) when x!=0;=0, when x=0 is continuous butnot differentiable at x=0