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