The number

One of the most important limits in the Calculus is

-.1 | -.001 | .001 | .01 | .1 | 1 | 5 | 10 | |||

2.8680 | 2.7195 | 2.7169 | 2.7048 | 2.5937 | 2.0000 | 1.4310 | 1.0096 |

As from the left, decreases and approaches as a limit. As from the right, increases and also approaches as a limit.

As , approaches the limit ; and as from the right, increases without limit.

Natural logarithms are those which have the number for base. These logarithms play a very important rĂ´le in mathematics. When the base is not indicated explicitly, the base is always understood in what follows in this book. Thus is written simply or .

Natural logarithms possess the following characteristic property: If in any way whatever,

david joyner 2008-11-22