The second one is the same, because the higher-order infinitesimal can be ignored in addition and subtraction, so the cubic power is ignored.
Infinitesimal is a concept in mathematical analysis. In classical calculus or mathematical analysis, infinitesimal usually appears in the form of function and sequence. ?
Infinitesimal is a variable whose limit is the number 0, which is infinitely close to 0. Specifically, when the independent variable x is infinitely close to x0 (or the absolute value of x is infinitely increased), the function value f(x) is infinitely close to 0, that is, f(x)→0 (or f(x)=0), then f(x) is called the infinitesimal amount when x→x0 (or x→∞). In particular, we should not confuse very small numbers with infinitesimal numbers.
Extended data:
Nature:
1, infinitesimal is not a number, but a variable.
2. Zero can be used as the only constant of infinitesimal quantity.
3. Infinitely small quantities are related to the trend of independent variables.
4. If the function is bounded in a hollow neighborhood, then G is called bounded quantity at that time.
For example, they were all infinitesimals at that time, all infinitesimals at that time, all bounded quantities at that time, and all bounded quantities at that time. In particular, any infinitesimal quantity must also be bounded.
5. The sum of finite infinitesimals is still infinitesimal.
6. The product of finite infinitesimals is still infinitesimal.
7. The product of bounded function and infinitesimal is infinitesimal.
8. Especially the product of a constant and an infinitesimal is also an infinitesimal.
9. The reciprocal of infinitesimal with non-zero constant is infinity, and the reciprocal of infinity is infinitesimal.
When the independent variable x tends to x0, the absolute value of the function increases infinitely, which is called infinity. Write it down. ?
Similarly, infinity is not a specific number, but an infinite development trend.
References:
Baidu encyclopedia-infinitesimal quantity