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What is the value of zero times infinity?
Zero times infinity is defined as "indeterminate".
Why is zero raised to zero an indeterminate form?
Because it does
What is infinity times infinity minus infinity?
Firstly, infinity is not a number (at least in lower level mathematics). You must instead use the language of limits to describe infinity. Using limits, a function which diverges to infinity multiplied by a function which diverges to infinity has a product which also diverges to infinity. However, taking this product, and subtracting away a function which diverges to infinity is "of indeterminate form". It might converge to zero, it might be diverge to positive infinity, it might diverge to negative infinity, or it might converge to a constant. In order to figure out which one of these possibilities applies, you must get the indeterminate form into the form infinity divided by infinity or 0/0 and then apply L'Hospital's rule. Edit: Just a pet peeve of mine. It's L'Hôpital, not L'Hospital. Even textbooks don't spell it right.
If division by zero is not defined then why do you consider inverse of zero as infinity in calculus?
Division by zero is not "not defined". Division is the repeated subtraction of one thing from another, counting the number of times you subtract. If you divide 15 by 3 you get 5. You can also subtract 3 from 15 5 times. If you subtract zero from something, that something does not change, so you could say that anything divided by zero is infinity. (End of answer to question asked, but....) By definition, a positive number divided by zero is positive infinity, and a negative number divided by zero is negative infinity. Also, what "is" not defined is zero divided by zero. We call that indeterminate. However, its not quite that simple. For example, 2x / x when x = 0 is indeterminate, but the limit of 2x / x as x approaches zero is very determinant: it is 2
Why is it not possible to divide by zero?
Their is no # that can be multiplied into 0 other than its self, therfore it is no defined value and is called an indeterminate form.
