Finding the limit analytically as x approaches 3 from the right

Question

lim (x->3 ) [-2/(x-3)]

Answer 1

Pick a number very close to "3" on the "right" side of it, say 3.00001. There is no real need to "analytically" rationalize this any further, as it satisfies the Direct substitution principle.

The idea behind this is to see the behaviour of the function as x decreases close to x = 3.