For example:
The power of 0 of any number is equal to1;
Any power of 1 is equal to 1.
Pay attention to these concepts in the limit.
0 and 1 in the limit are different from 0 and 1 in elementary mathematics.
0 and 1 in limit theory are just figures of speech.
When the denominator is not 0, it cannot be substituted casually. It depends on whether 1 is an infinite power. Is it a power of 0? If so, it is irreplaceable; If not, it can be replaced.
Even if the denominator is 0, the substitution must be infinite, whether it is positive infinity or negative infinity. You can boldly write limit = +∞, or -∞.
The basic methods for finding the limit are:
1, in the fraction, the numerator and denominator are divided by the highest degree, and infinity is calculated as infinitesimal, and infinitesimal is directly substituted into 0;
2. When the infinite root is subtracted, the molecule is physical and chemical, and then the method in (1) is used;
3. Apply two special restrictions;
4. Apply L'H?pital's law, but the application condition of L'H?pital's law is that it is transformed into infinity ratio or infinitesimal ratio, and the denominator of the numerator must also be a continuously derivable function. It is not invincible and cannot replace all other methods. The first floor is exaggerated.
5. The expansion is based on McLaughlin series, but it is generally misinterpreted as Taylor expansion in China.
6. Equal-order infinitesimal substitution, which is very popular in China, is relatively calm abroad. Because it is not a teaching method worth popularizing; Second, you often make mistakes, so be especially careful.
7. Extrusion method. This is not a universal method, because it is impossible to get the same result after zooming in and out.
8, under special circumstances, into the integral calculation.
9. Other methods that are extremely special and cannot be widely used.