Regarding the equivalent infinitesimal and those two important limits, the equivalent infinitesimal is equivalent to the substitution of some limit expressions, and the limit value is not found exactly. After replacement, it is still operated together with the limit expression of the whole, and (1+ 1/x) x directly finds the value of this part of the limit and substitutes it into the operation.

You can understand it this way, that is, the chemical reaction process of two substances AB. Component b in b must be fully combined with component a in a to get the desired result, but now you have picked out component b and let component b react with other components in a first, and then the obtained substance reacts with component a.

Although we got some results, we didn't realize the real utilization of component A. We could have got one gram of gold, but now we got two grams of silver. You think you have reached the limit, but in fact you haven't.

Or just remember that you don't need two important limits to kill, and when you encounter a power exponent, it becomes the ln power of e.

The origin of limit:

Like all scientific thinking methods, extreme thinking is also the product of abstract thinking in social practice.

The idea of limit can be traced back to ancient times. For example, the secant technology in Liu Hui, the motherland, is an original and reliable application of the limit idea of "approaching constantly" based on the research of intuitive graphics; The ancient Greeks' exhaustive method also contained the idea of limit, but because of their "fear of infinity", they obviously avoided artificially "taking the limit" and completed the relevant proof by indirect proof-reduction to absurdity.

/kloc-in the 6th century, Steven, a Dutch mathematician, improved the ancient Greek exhaustive method in the process of investigating the center of gravity of a triangle. With the help of geometric intuition, he boldly used limit thought to think about problems and gave up the proof of reduction law. In this way, he inadvertently "pointed out the direction of the development of the limit method into a practical concept."