An equivalent infinitesimal is ln( 1+x)~x, so ln (1+x n) ~ x n.

The algorithm of ln function: ln(MN)=lnM+lnN, ln(M/N)=lnM-lnN, LN (m n) = NLnm, ln 1=0, lne= 1. Note that after disassembly, m and n need to be greater than 0. Without ln(M+N)=lnM+lnN, and ln(M-N)=lnM-lnN, lnx is the inverse function of e x.

The general form of logarithmic function is y=㏒(a)x, which is actually the inverse function of number function (two functions that are symmetrical about each other's straight line y = x = a y), and can be expressed as x = a y. Therefore, the adjustment of a in exponential function (a >；; 0 and a ≠ 1).

The basic methods for finding the limit are:

1. When the numerator and denominator in the fraction are divided by the highest degree, infinity is calculated as infinitesimal, and infinitesimal is directly substituted into 0.

2. Minus infinite roots, molecules are physical and chemical.

3. Apply the Lobida rule, but the application condition of the Lobida rule is that it is transformed from infinity to infinity or infinitesimal to infinitesimal, and the numerator denominator must also be a continuous derivative function.