Polynomial functions and rational functions.

When gets either positive or negative with arbitrary large absolute value, every fraction has limit equal to 0, thus the sum in parentheses has limit equal to 1, whence the result.

The same kind of computation can be useful for non polynomial expressions, as shown in the next example.

Thus .

where and . We push out the greatest power of in the numerator and the greatest power of in the numerator:

Now every fraction and every fraction has limit equal to 0 when gets either positive or negative with arbitrary large absolute value, therefore both expressions in parentheses have a limit at equal to 1, whence the result.

Noah Dana-Picard 2007-12-28