Powers.

Now take two functions and defined over the same neighborhood of the real number (resp. of , resp. of ). Consider the function defined over by . The different cases appearing when computing limits for at are displayed in the following table:

Theorem 4.4.4

 0 0 0 undeterminate 0 1 undeterminate

One of the most important cases to remember is the following:

Theorem 4.4.5

Using this theorem and the algebraic properties we studied previously, many exercises are now solvable.

Example 4.4.6
1. Compute the limit at of .

Solution: we have

By an easy substitution we show that

whence

2. By a similar way, we show that

Noah Dana-Picard 2007-12-28