I think it is zero because ANYTHING times 0 equals 0
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Yes. In such a case, manipulate the problem so that you get the indeterminate form 0/0 or infinity/infinity, then proceed with l'Hopital's Rule.
5 times 5 divided by 5 times 0 equals infinity or undefined. Division by zero is undefined
Because zero multiplied by any number is always zero, but anything multiplied by infinity is infinity. Zero times infinity is being pulled both ways. Also, the definition of infinity is any number x divided by 0. When you multiply zero by infinity, the zeroes "cancel out", leaving absolutely nothing behind.
If you mean 1 x 0, that's 0, not infinity.
An unknown number x times infinity would be infinity.