Question

What does the value of f(x)=(1+1/x)^x approach as x approaches infinity?

Answer 1

In order to determine the value of f(x) as x approaches to oo, replace larger values of x into the function and identify the tendency of f(x), as follow:

x = 1000

$f(1000)=(1+\frac{1}{1000})^{1000}\approx2.7169$

x = 1000000

$f(1000000)=(1+\frac{1}{1000000})^{1000000}\approx2.7182$

x=1000000000

$f(1000000000)=(1+\frac{1}{1000000000})^{1000000000}\approx2.7182$

As you can notice, as x approaches to oo, f(x) approaches to 2.7182..., which is the value of constant e.

answer: e