Show that f haven’t primitives.f=0, x=0f=0, x=0

Show that f haven’t primitives.f=0, x=0f=0, x=0

Show that f haven’t primitives.f=0, x=0f=0, x=0

You need to test the continuity of the given function at x = 0 such that:`lim_(x->0, x< 0) (sin(1/x)-(1/x)cos(1/x)) = oo“lim_(x->0, x>0) 0= 0“f(0) = 0`Since `lim_(x->0, x< 0) (sin(1/x)-(1/x)cos(1/x)) = oo != 0 = lim_(x->0, x>0) 0` , then the function is not continuous at x=0, hence, it is not differentiable at x=0 and it has no primitives at x = 0.