Maxima can compute limits for a wide range of rational and transcendental functions.
For rational functions, it is often important to know the value at inifinity:
limit ((x^2 - 1)/(x^2 + 1), x, inf);
1
The value of a "0/0" expression can be easily computed:
limit ((x^2 + x - 6)/(x^4 + x^3 - 19*x^2 + 11*x + 30), x, 2);
5 - -- 21
Occasionally a limit from the right side differs from the limit from the left side at the same point:
limit (tan(x), x, %pi/2, plus);
minf
This is the limit from the right side: It is taken for values %pi/2 + epsilon for increasingly small positive values of epsilon. Maxima finds the limit value minus inifinity.
When we take the limit at the same point from the left, we obtain:limit (tan(x), x, %pi/2, minus);
inf
We can also try to compute that limit without telling Maxima fromwhich side we want to compute it:
limit (tan(x), x, %pi/2);
und
This answer means undefined. This is a hint that we should compute the limit from both sides.
Here is a different example:
limit (tan(3*x)/tan(x), x, %pi/2);
1 - 3