(2x-6)/abs(x-3)

Question

when x aproaching 3 from the left

Answer 1

If x is approaching 3 from the left, then x < 3, so x-3 < 0

 

Therefore, l x-3 l = -(x-3)

 

So, lim_x→3^- [(2x-6)/ l x-3 l ]  = lim_x→3^- [2(x-3)/(-(x-3))]

 

                                        = lim_x→3^- (-2) = -2