When deriving, for example, the final result is (2+delta x ), and then delta x approaches 0, so 2+delta approaches 2. The final derivative is 2, so this 2 is Is it available?
If not, shouldn't the final result be infinitely close to 2 instead of 2?
If it is possible, does it mean that the function y=one part of x, when x approaches negative infinity, y approaches 0, and finally can also be taken to 0?
See Zhihu answer:
The limit may not necessarily be reached. For example, the sequence 0.9, 0.99, 0.999,..., the limit 1 cannot be obtained. Another example is the sequence 1,1,1,1,1,..., the limit 1 can be obtained. So the question "can" or "can't" is not accurate. In addition, it is no different from Newton's time now, and "limit" has become a strictly defined mathematical term, rather than a cloudy thing based on intuition. For example, the sequence 0.9, 0.99, 0.999,..., if you are a high school student who has never studied calculus and perceive the limit only by intuition, the following two statements seem to make sense and can be understood through "intuition": this sequence The limit of is infinitely close to 1. The limit of this sequence is 1. However, it only takes a little further thought to know that the second statement should be used. Because the word "infinitely close" in the first statement is really in the clouds, and such a definition of the limit is not conducive to in-depth research. Of course, it's fine if you think so. But whatever you think, the word "limit" is now defined, and we must use it as defined. It must be clear: 1. This sequence is infinitely close to 1, 2. The limit of this sequence is 1.
Source: Zhihu https://www.zhihu.com/question/575299191/answer/2826264648