High math homework solution helps, high math urgently asks for a solution from God

1.If there is a Taylor series, does the Taylor series necessarily converge to the function f(x) in the neighborhood of a number?

A: Not necessarily. The fact is that if a Taylor series corresponding to f(x) is obtained, and the Taylor series is convergent, in this case, there is no guarantee that the Taylor series will converge to the function f(x).

In other words, it is possible that the sum function of this convergent Taylor series is another s(x) different from f(x). Then, to ensure that the Taylor series of this convergence converges to the function f(x), i.e., the sufficient and necessary condition for f(x) as its sum function is that "the Lagrangian remainder term in F(x)'s Taylor formula is zero at the limit of n->". Let's call the convergence of this Taylor series and the convergence of this function f(x) as "f(x) can become a Taylor series".

Notice that this is what "achievable" means.

2.Answer: If f(x) has derivatives at x0=0, then you can make a McLaughlin series corresponding to f(x), and that's it.

As for "whether the series can converge within a certain interval and whether it converges in f(x), it needs to be further investigated." Further, even if the series converges to the function s(x), s(x) is not necessarily f(x), as in problem 1.

3 The sentence "Only f(x) can first form a Taylor series, and then there is a McLaughlin series, and converge to f(x) in the neighborhood where x0=0 exists."

Give yourself a little confidence, as long as you want to learn well, there is no bad learning, only if you don't want to learn, you can't learn well.

Make good use of this summer vacation, go back to school to be serious, talk to the teacher, chat, and the teacher will give you a lot of advice.

I usually spend a little more time in mathematics, and I don't know what to do, so I look for a teacher, and if I don't know how to do it, I look for a teacher, anyway, the teacher is the best helper.

Remember! Remember!

A simple calculation is sufficient, and the answer to the head of the limb celery calendar is shown in the first life picture.

It is converted into Green's formula, and then the polar coordinate commutation method is used.

The result of the third question is obviously 0

The result in ** is wrong.

The following omit lim (x 0):

x^(sinx)

e^[ln(x^(sinx))]

e^[(sinx)(lnx)]

e [(lnx) (1 sinx)] (for type, using Robida's rule) e e

e^[-tanx]e^0