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Exponential Limits


In this case, and represents the basis of natural or neperian logarithms. It's the irrational number and whose approximate value is 2,7182818.
See the table with values ​​of x it's from .

x

123101001 00010 000100 000

22,252,37032,59372,70482,71692,71812,7182

We note that as .
Similarly, making the replacement we have:

Even more generally, we have:

The above two forms give the immediate solution to exercises of this type and avoid algebraic substitutions.

If ,So .
But:

Soon:

How x 0 then u 0. Therefore:

Generalizing the above property, we have .

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