1, the formula of the first important limit:

lim sinx/x = 1(x-& gt； 0) When x→0, the limit of sin/x is equal to1; Pay special attention to the fact that when x→∞, 1/x is infinite, the limit obtained from the property of infinitesimal is 0.

2. The second important limit formula:

Lim (1+ 1/x) x = e (x→∞) When x →∞, the limit of (1+1/x) x is equal to e; Or when x→0, the limit of (1+x) (1/x) is equal to e.

Have nature:

1, Uniqueness: If the limit of a series exists, the limit value is unique, and the limit of any of its subsequences is equal to the limit of the original series.

2. Boundedness: If a series converges (has a limit), then the series must be bounded. However, if a series is bounded, it may not converge.

3. Relationship with subsequences: sequence {xn} converges or diverges with any trivial subsequence, and has the same limit when converging; The necessary and sufficient condition for the sequence {xn} to converge is that any nontrivial subsequence of the sequence {xn} converges.