limit computes the limit of an expression at a finite or infinite point.
It is also possible with an optional argument to compute a one-sided
limit (1 for the right limit and -1 for the left limit).
limit takes three or four arguments :
an expression, the name of a variable (for example x), the limit point
(for example a) and an optional argument, by default 0, to
indicate if the limit is unidirectional.
This argument is equal to
-1 for a left limit (x<a) or is equal to 1
for a right limit (x>a) or is equal to 0 for a limit.
limit returns the limit of the expression when the variable (for example
x) approaches the limit point (for example a).
Remark
It is also possible to put x=a as argument instead of x,a, hence :
limit takes also as arguments an expression depending of a variable,
an equality (variable =value of the limit point) and perhaps 1 or -1 to
indicate the direction.
Input :
or :
Output :
Input :
or :
Output :
Input :
or :
or :
Output :
Hence, abs(1/x) approaches +∞ when x approaches 0.
Exercises :
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2/2)-exp(x/2))/((1-cos(x))*sin(x)),x,0)Remark
To compute limits, it is better sometimes to quote the first argument.
Input :
Note that the first argument is quoted, because it is better that
this argument is not simplified (i.e. not evaluated).
Output :