Current location - Training Enrollment Network - Mathematics courses - Limit calculation in advanced mathematics
Limit calculation in advanced mathematics
If this is a big problem, try not to omit it. Mathematics needs rigorous deduction.

It doesn't matter if you fill in the blanks or choose something. After all, you don't look at the steps.

Because it is not convenient to type the compound function here, I made the following substitution to facilitate the following description.

First of all, the principle here is not that the product of bounded function multiplied by infinitesimal is infinitesimal.

The first step of the answer actually means that B is the high-order infinitesimal of A, that is, B=o(A).

When x→0, A+O (a) = A. This principle will be called "higher-order absorption" in some postgraduate courses. Of course, you can also think that this is an infinitesimal equivalent, that is, A+O (a) ~ A.

In addition, the conclusion of "high-order absorption" is generally used by people with a high number of 6. This question is not bad. In some complicated problems, if the high math level is not very good, it is easy to roll over. If the subject wants to use it, it must be thoroughly understood.

As for the question of whether to deduct points for specific questions, after all, I don't know the grading standard of the paper, but I think it's not good for you to take 3x^2 directly without giving an explanation in the big questions.

There is also the algorithm lim(a/b)=lima/limb, which cannot be directly used here. The premise is that the denominator is ≠0, which is obviously infinitesimal =0, so it is wrong to write a big question like this if "the product of bounded function multiplied by infinitesimal is infinitesimal", so I think it is easy for the reviewers to mistake you for using the wrong rules by writing 3x^2 directly.