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:
One of the most important cases to remember is the following:
Using this theorem and the algebraic properties we studied previously, many exercises are now solvable.
Example 4.4.6
- Compute the limit at
of
.
Solution: we have
By an easy substitution we show that
whence
- By a similar way, we show that
Noah Dana-Picard
2007-12-28