Question 2: Who can tell me what the idea of limit is? Alas, the idea of limit is really hard to understand. Limit is an important idea in modern mathematics. Mathematical analysis is a subject that studies functions with the concept of limit and limit theory (including series) as the main tools.
The so-called limit thought refers to a mathematical thought that uses the concept of limit to analyze and solve problems. The general steps of solving problems with limit thought can be summarized as follows: for the unknown quantity under investigation, first try to conceive a variable related to it, and confirm that the result of this variable through infinite process is an unknown quantity; Finally, the results are obtained by limit calculation.
The idea of limit is the basic idea of calculus, and a series of important concepts in mathematical analysis such as continuity, derivative and definite integral of function are defined by means of limit. If you want to ask, "What is the theme of mathematical analysis?" Then it can be summed up as follows: "Mathematical analysis is a subject that studies functions with extreme ideas".
Let the function f(x) be defined in the centripetal neighborhood of point X. If there is a constant A, there is always a positive number δ for any given positive number ε (no matter how small), so when X satisfies inequality 0, Question 3: What is the limit idea of instantaneous velocity? What is the instantaneous speed? V=S/t, but t is very small in an instant. How small is it? 0? ...
The theory of differentiation here is that this time is very small, not zero, but close to zero, as long as it is within the allowable range of error.
Then the instantaneous speed means that the distance from T to t+0.000 1s (small enough) can be understood as the instantaneous speed at that moment. This limit idea combined with differential theory can prove that this is correct.
Question 4: What can you learn from extreme thoughts? What about calculus? Limit is a very basic tool, which leads to differentiation, while calculus is essentially the addition of the same elements.
Question 5: What is the relationship between extreme thinking and calculus? Limit is the foundation of calculus. The basic definitions and operations of differential calculus and integral calculus are all obtained on the basis of limit. So only by mastering the basic idea of limit can we really understand and learn calculus well.