URGENT ONE SIDED LIMITS

Question

find the one sided limit at the point x=0 for function

f(x)=(|x|-x)/x x≠0

Answer 1

If x < 0, then lxl = -x

 

So, lim_x→0- [(lxl - x)/x] = lim_x→0^- [-2x/x] = -2

 

If x > 0, then lxl = x

 

So, lim_x→0⁺ [(lxl - x)/x] = lim_x→0⁺ [0] = 0

Answer 2

at x=0, f(x) is undefined as any division by 0 (zero) yields results that cannot be defined.