# Evaluate limit as x approaches 0 of (1-cos(x))^x

Use the properties of logarithms to simplify the limit.
Rewrite as .
Expand by moving outside the logarithm.
Move the limit into the exponent.
Consider the left sided limit.
Make a table to show the behavior of the function as approaches from the left.
As the values approach , the function values approach . Thus, the limit of as approaches from the left is .
Consider the right sided limit.
Make a table to show the behavior of the function as approaches from the right.
As the values approach , the function values approach . Thus, the limit of as approaches from the right is .
Anything raised to is .
Evaluate limit as x approaches 0 of (1-cos(x))^x