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

Question

its meant to be x--> 2 from the left (or down or whatever - means)

Answer 1

the function is this:F(x)=1/(e^x/(2-x)-1)??? Then Lim(x->2-)F(x)=1/0-=-infinity

Answer 2

The x --> 2 means "as x gets close to 2" from any direction.

If the function is 1/(e^(x/2-x)-1)
then the first thing to do is see if this function exists at x = -2:
1/(e^(2/2-2)-1) = 1/(e^(-1) - 1)
which is defined for x = -2. So this makes the limit easy. All you have to do is figure out what e^-1 is and the rest is clear. I used excel to get e^-1 = .368
so the answer is 1/(.368-1) or 1/-.632 = 1.58

Answer 3

graph it. look from the left, as x approaches 2, what y value correespond to that x value?
-1.582

Answer 4

= e/(1-e)
= -1.5819