Lim (x--->+2) e^[3/(2 - x)]?

Question

Can someone help me understand how to find this limit.
The answer is actually 0.

Thank you.

so basically e^(-infinity) = 0 ??
what is e^(infinity) = ?

thank u for taking ur time.

Answer 1

as x goes to 2 from the right...
... (2-x) goes to 0 from the negative values ...
thus 3/(2-x) goes to 3/(0-) ... or that is negative infinity. §

now observe the graph of the exponential function,
it is asymptotic to the negative x-axis.
thus e^[3/(2-x)] goes to zero.
since as you go to the left of the graph of the exponential, the value becomes zero. (going to the left is going to negative infinity)

Answer 2

Lim (x--->+2) e^[3/(2 - x)]
When x --> +2 from the left, the expression goes to infinity and there is no limit
When x --> +2 from the right the limit is 0
You should have stated that x --> 2+ which means x --> approaches 2 from the right.

So if (2-x) is always negative as x --> 2+ and the closer it gets to 2, the larger a negative number 3/(2-x) becomes. So the at x= 2.01, f(x) = 0 as far as the calculator is concerned.