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+(1)/(1000))^(1000)\approx2.7169`

x = 1000000

`f(1000000)=(1+(1)/(1000000))^(1000000)\approx2.7182`

x=1000000000

`f(1000000000)=(1+(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