Limit Question: Calculator Discrepancy

[Taiki_Kazuma]

Question: Why does my calculator state the limit of the following function is 1, but my calculations state it does not exist?

There's a gap in the graph between -1 and 0. I noticed that there are a few points in that section that do generate real values which appear to move towards 1, but is this enough information to presume the limit is 1 at 0?


t(x) = (1 + [1/x])^x

lim t(x) = ??
x->0


Chart:
x-value____t(x)-value
1_________2.000000
.5________1.732051
.1________1.270982
.01_______1.047233
.001______1.006933
.0001_____1.000921
.000001___1.000014
-.000001___0.999986 - 0.000003i
-.0001_____0.999079 - 0.000314i
-.001______0.993112 - 0.003120i
-.01_______0.954617 - 0.030000i
-.1________0.763453 - 0.248061i
-.5________-i
-1_________undefined

 

[LCKurtz]

What is true is that the one sided limit as x → 0⁺ is 1.