Limit of (1+x)^(1/x) as x approaches 0
How to show the limit of (1+x)^(1/x) is equal to the constant 'e'
Begin by letting a variable equal to the limit, then apply the natural logarithm to both sides of the equation. The goal is to reduce the limit expression on the right hand side into the constant e.
This process is achieved by using a few log laws in conjunction with L'Hopital's rule. The limit is important in differentiating e^x from first principles, as such it is usually taken as an identity and this tutorial is simply trying to show the relation between the limit and the constant e.
Music by Adrian von Ziegler
