Quote:
Originally Posted by Kristi
You are using limits to describe finite concepts.
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A limit can be applied anywhere. A limit only exists when the limit is finite, anyway. This statement really confuses me.
Quote:
Originally Posted by Kristi
Limit definitions are solid when finite definitions do not exist, eg diving by zero.
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But you keep saying 0/0 = 0. 0 is neither -infinity nor infinity, so it is finite.
Quote:
Originally Posted by Kristi
Generally speaking, you apply the limit to the modifying operation, eg division, raising to a power, etc.
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Each of the limits above are valid for evaluating 0/0. The "modifying operation" is rather ambiguous in this case. 0/0 could be split up to 0*1/0, or any other number of ways and we'd have a few operations to choose from.
Depending on how we approach 0/0, we can get infinitely different answers. Consider the equation (3x^2+
nx)/x. At x=0, we have 0/0, and there is a removable discontinuity, but we can still evaluate the limit and it gives us
n.
The function happens to be continuous. If we say that 0/0 = 0, we've broken the continuity.