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 .

| 1 | 2 | 3 | 10 | 100 | 1 000 | 10 000 | 100 000 |

2 | 2,25 | 2,3703 | 2,5937 | 2,7048 | 2,7169 | 2,7181 | 2,7182 |

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 .