
limit - limit of expressions

Calling sequence:
limit(expr, x[ =v ]  [ ,dir ])

Parameter:
expr   --  expression
x      --  identifier
v      --  expression
dir    --  Left or Right

Summary:

The call limit(expr,x=v) computes the limit of the expression expr when x
goes to v. The default point is v=0. The call limit(expr,x=v,Right) (resp.
Left) gives the limit when x goes to v from the right (resp. from the left).
When both limits (from the left and from the right) are different, it returns
undefined.

The limit function uses series , and returns FAIL if the order of the expansion
computed is not sufficient. In this case, it may be needed to increase the value
of the global variable ORDER (see series ) in order to find a limit.

When the limit can not be computed, it returns unevaluated.

The algorithm based on the dissertation of Dominik Gruntz: "On Computing
Limits in a Symbolic Manipulation System", submitted to the SWISS FEDERAL
INSTITUTE OF TECHNOLOGY ZUERICH in 1995.

>>  limit((1-cos(x))/x^2,x);

      1/2

>>  limit((1+1/n)^n,n=infinity);

      E

>>  limit((sin(tan(x))-tan(sin(x)))/x^7,x);

      FAIL

>>  ORDER:=8: limit((sin(tan(x))-tan(sin(x)))/x^7,x);

      - 1/30

>>  limit(1/x,x=0), limit(1/x,x=0,Left), limit(1/x,x=0,Right);

      undefined, - infinity, infinity

>>  limit((exp(x*exp(-x)/(exp(-x)+exp(-2*x^2/(x+1))))-exp(x))/x,x=infinity);

      -exp(2)

See also:  series

