The method of finding the limit of postgraduate mathematics is as follows:

1, find the limit by definition.

2, using Cauchy criterion to find.

Cauchy criterion: {xn} has a limit if and only if it is given ε >; 0, there is a natural number n, so when n >; When n is

Any natural number m has | xn-XM | < ε.

3. Find the limit by using the operational nature of the limit and the known limit.

Such as lim (x+x 0.5) 0.5/(x+ 1) 0.5.

=lim(x^0.5)( 1+ 1/x^0.5)^0.5/(x^0.5)( 1+ 1/x)^0.5

= 1.

4. Using inequality, that is, pinch theorem.

5. Use variable substitution to find the limit.

For example lim

(x^ 1/m- 1)/(x^ 1/n- 1)

Let x = y Mn

Get: = n/m。

6. Find the limit with two important limits.

( 1)lim

sinx/x= 1

Fairy fairy-> 0

(2) Linear motor

( 1+ 1/n)^n=e

Yi-> ∞

7, using monotone bounded limit.

8. Use the property of function continuity to find the limit.

9. Use the Robida rule, which is used the most.

10, using Taylor formula, which is also very common.