How to | Compute a Limit
Even simple-looking limits are sometimes quite complicated to compute. The Wolfram Language provides functionality to evaluate several kinds of limits.
Use Limit to calculate limits; the first argument is the function and the second has the form variable->value . You can expect that 
:
Limit[(1 + 1 / n) ^ n, n -> Infinity]You may want to calculate limits from the right or left. For example, although 
is not well defined, the Wolfram Language defaults to limits from the right:
Limit[1 / x, x -> 0]Limit[1 / x, x -> 0, Direction -> -1]To force the limit to be from the left, use Direction->1:
Limit[1 / x, x -> 0, Direction -> 1]If you know something about a parameter in a limit, use the Assumptions option to include this information.
Suppose you want to calculate 
. Without knowing more, the limit cannot be calculated:
Limit[x ^ n, n -> Infinity]If, however, you know that 
, then you can compute the answer:
Limit[x ^ n, n -> Infinity, Assumptions -> 0 ≤ x < 1]