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Zero in the numerator

If in a fraction the numerator is zero and the denominator is unequal zero, the result is zero. That we learned already in school.

 


Explanation

You can check that

 ,    ,    ,  etc.

The fraction

gives the same result, but you cannot check it, as there is no  ∞  key on your calculator. Infinity is not a number. Yet, we think the result is quite logic. Now we investigate what the fraction

will produce. We know that Δx approaches zero, but it is not zero, and therefore the division is permitted. So the answer must be 0. Yet again, you cannot check it, as there is no  Δx  key on your calculator.

 


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