Asked by Dylan Brow
Find one sided limit
lim x->2+ 1/(1+e^(1/x-2))
lim x->2+ 1/(1+e^(1/x-2))
Answers
Answered by
MathMate
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
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