A reason you might want 00 to be something other than 0 or 1 As the number x increases t...

A reason you might want 0⁰ to be something other than 0 or 1 As the number x increases through positive values, the numbers 1/x and 1/(ln x) both approach zero. What happens to the number

as x increases? Here are two ways to find out.

a. Evaluate ƒ for x = 10, 100, 1000, and so on as far as your calculator can reasonably go. What pattern do you see?

b. Graph ƒ in a variety of graphing windows, including windows that contain the origin. What do you see? Trace the y-values along the graph. What do you find?