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Depending on the context in which the problem arises, 0 1 0 = ∞ may be a valid answer.
No not consistent since you took the limit as x approaches 0 from the left. If you took the limit from the right, you approach − ∞ . So the answer must be undefined.
That's assuming 0 1 0 arises from x → 0 lim x 1 0 . Which indeed would mean the limit wouldn't exist.
However, there are other contexts in which it could arise. For example, x → ∞ lim x 2 1 0 = 0 . Additionally, we don't even need a limit. If we're dealing with the real projective line (which adds a formally-defined "point at infinity") we don't even need a limit to write ∞ 1 0 = 0 .
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If 10/2 (which is five) is multiplied by two, it becomes 10, the previous numerator. Same with any other fraction where a number is divided by a number, x, and once again multiplied by x. In this case, if 10/0 is multiplied by 0, it should be ten according to the rule I previously stated, however, another rule also states that anything multiplied by 0 is 0. Therefore, it is undefined.