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 to 1.

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.

Extended data:

"Limit" is the basic concept of calculus, a branch of mathematics. The "limit" in a broad sense is "infinitely close and never reached".

The "limit" in mathematics means that a variable in a function gradually approaches a certain value A in the process of getting bigger (or smaller), and "it can never coincide with A". The change of this variable is artificially defined as "always approaching" and has the trend of "constantly approaching point A".

Limit is a description of "changing state". The value a that this variable always approaches is called the "limit value" (of course, it can also be expressed by other symbols).

Limit solution:

1, continuous elementary function, to find the limit in the definition domain, you can directly substitute this point to get the limit value, because the limit value of continuous function is equal to the function value of this point.

2. Eliminate zero factor by using identical deformation.

3. Use the relationship between infinity and infinitesimal to find the limit.

4. Find the limit by using the property of infinitesimal.

5. The original formula can be simplified and calculated by using equivalent infinitesimal replacement to find the limit.

6. Use two limit existence criteria to find the limit, and some topics can also be enlarged and reduced, and then use the pinch theorem to find the limit.

Baidu Encyclopedia-Limit (Calculus Concept)