State your answers to 5 decimal places.

Question

Consider f(x) = (1 + x ) ^-1/x

x	f(x)	x	f(x)
-0.1	0.34868	0.1	0.38554
-0.01	0.36603t	0.01	0.36971
-0.001	0.36769	0.001	0.36806
−0.0001	0.36786	0.0001	0.36789

Looking at the values, we can estimate that lim f(x) = _____

^{x -> 0}

Answer 1

What you can suspect is that the limit is between .36786 and .36789.

I see no simple way to estimate the 5th digit more accurately.

However, the limit you are looking at by definition is e^-1 = .367879 by my calculator.