Advanced Mathematics | Some methods of finding limits

When clearing your computer disk and organizing your notes, make a note of it.
The content is relatively simple and is used for review and review without in-depth study.

algorithm

The premise of use is: $\lim f(x)=A,\lim g(x)=B.$

Two important limits

$$\underset{x\to 0}{\lim }\frac{\sin x}{x}=1$$

2. $$\underset{x\to \infty }{\lim }(1+\frac{1}{x}{)}^x=e$$

Equivalent to infinitesimal

Equivalent infinitesimals can generally be replaced as factors of multiplication and division, and can be replaced under certain conditions in addition and subtraction relationships. (According to my experience, certain conditions refer to the fact that the result of the operation with other monomials after substitution is not 0) The
commonly used equivalent is infinitesimal, when $x\to 0$ o'clock

Muke Jullin official:

The replacement of McLaughlin's formula is similar to the replacement of infinitesimals, except that accuracy issues need to be considered, and higher-order infinitesimals cannot be easily ignored.
Follow two principles: 1. The upper and lower fractions are of the same order; 2. The addition and subtraction of powers are the lowest.

Several common Maclaurin formulas:

Lópida's Law

Prerequisites for use:
(1) limf(x)=limg(x)=0(∞)
(2) $\lim \frac{f^{{}^{\prime }}(x)}{g^{{}^{\prime }}(x)}$exists
Then: $\lim \frac{f(x)}{g(x)}=\lim \frac{f^{{}^{\prime }}\left(x\right)}{g^{{}^{\prime }}\left(x\right)}$

Lópida's rule is often used to find infinitives: $\frac{0}{0}$and $\frac{\infty }{\infty }$You can relate the slope to 0 and ∞ \inftyUnderstand the relationship between tangents and secants at$\infty \; .$For other forms,$0\cdot \infty ，\infty +\infty ，1^{\infty }...$ and so on, can be converted into infinitives through common fractions, exponents, etc.

slightly

cy here, I will add some other methods later when I have time.