What is 0 to the 0 is it one

we didnt get to finish this part in class
what about infinity times 0

0^0 is definitely not 1. It is called an indeterminate form, usually investigated in a first-semester calculus class by use of L'Hopital's rule. Its value depends on investigating a limit using an algebraic manipulation and L'Hopital's rule. That value could turn out to be anything from negative infinity to positive infinity and anything in between.

The same is true of zero times infinity. It is neither zero nor infinity. You need the same tools from calculus to find its value.

And Elizabeth, C Stevens, and Ramandeep are all incorrect in their answers.

It is an indeterminate form.

When you get to "Hospital's rule" in calculus, 0° form will often turn out to be 1, but sometimes it will come out to be something else. It is all abut limits.


Basically if lim f(x) = 0 and lim g(x) = 0, then what is

...........g(x)
lim f(x) ...... = ???

The "form" says 0° but the limit sometimes can turn out to be anything, depending on the functions.

The rule in algebra is -not- "anything" to the zero power. The rule is,

If a ≠ 0, then a° = 1. Many students learn "half a rule." Kudos on questioning this.

Also, infinity is not a number. The rule says if a is a real number then a•0 = 0•a = 0. Since ∞ is not a number, that rule does not apply either. ∞•0 is another indeterminate form. Using forms (this is not rigorous) 1/0 = ∞, so ∞•0 = 0/0 which you know is indeterminate. (This is just a way for you to remember it and see that is is "reasonable.")

0^0 is undefined or indeterminate, but it proves very useful to consider it to be 1in many instances!

See:
http://www.askamathematician.com/2010/12…

Infinity times zero is undefined or indterminate.