Find one sided limit

Question

lim x->2+ 1/(1+e^(1/x-2))

Answer 1

Missing Parentheses:
1/(1+e^(1/x-2)) should read: 1/(1+e^(1/(x-2)))

Lines below are not rigorous, but demonstrate what happens.

For x->2+
1/(1+e^(1/(x-2)))
=1/(1+e^(1/0+)))
=1/(1+e^∞)
=0

For x->2-
1/(1+e^(1/(x-2)))
=1/(1+e^(1/(0-)))
=1/(1+e^(-∞))
=1/(1+0)
=1