The limit of the number series is a question for judging whether it is true or false, why did I misc

1. The definition of the limit of the sequence is an arbitrarily small positive number.

Answer: True. Only when it can be arbitrarily small can it be said that it is infinitely close, that is, the existence of the limit.

2. There are infinitely many n in the limit of the sequence, but it is enough to find one.

Answer: True. As long as n is greater than n, the inequality holds, and there are an infinite number greater than n, all of which can be n.

3. If there is a limit to a sequence, then the limit is unique.

Answer: True. Even if it is fluctuating, it is not considered a limit, but can only be said to be bounded.

4. With |an-a|< The equivalent is that an belongs to (a- ,a+) solution] right. This is a fundamental property of inequality.

5. The limit of the sequence is a, which means that there are infinite terms in (a- ,a+) and infinite terms outside (a- ,a+).

Answer] False. There are infinite multinomials within (a-,a+) and finite multinomials outside (a-,a+).

1. Lack of absolute value.

2. This sentence is good, but it cannot be used as a definition of the limit of the number series because it is not comprehensive enough. An infinite number of items does not represent all xn. For example, xn converges but x2n spreads and satisfies the infinite number xn so that the inequality holds, but the sequence is still divergent. All right.

(5) 1 Polynomial type When the denominator and numerator number are the same, the limit value is the ratio of the highest order coefficient.

7) N, 1 n 0, cos0 = 1, so the limit is 1

The limit value when approaching infinity is much simpler.

You're really an excellent young man, let me tell you, the law of Lobida is used when it is the last resort, and generally the law of Lobida does not apply, its use conditions are very limited, and you know that there is a problem at a glance. There are many ways to find the limit, and the pinch criterion is a very common usage, especially in the part of finding the limit of the number series, which is commonly used to solve the pinch criterion, and it is also very common in the postgraduate examination papers. For the questions, you can refer to my example 3 questions to do (a little different, similar, can be used as a reference).

Take a closer look at the conditions of use of the Nobida Rule.

is the numerator denominator = 0 0 or

Such a large list, separate from each other, obviously does not work.

The sufficient and necessary condition for the existence of the limit is that the left limit is equal to the right limit, and the left limit in this problem is not equal to the right limit, so the limit does not exist, so the conclusion in the question is wrong.

Since it is not mentioned in the title that the limits of these two sequences exist, it is obviously wrong to find the limits of xn and yn without this premise.

For example, when xn = n + and yn = -2n, there are also 2xn + yn = 1, but the limits of xn and yn do not exist.

Under the premise that the limit of 2xn+yn mentioned in the title is 1 and the limit of xn-2yn is 1, it will not be a problem to indirectly make up the limit of xn yn.

The first limit of the square gets.

4x2+4xy+y2=1……(1)

The second limit of the square is obtained.

x2-4xy+4y2=1……(2)

The two limits are multiplied to obtain.

2x2-3xy-2y2=1……(3)

1)-(2))*2 3-(3)=25 3*xy=-1 gives xy=-3 25

The limit of the sum difference of the series exists, but the limit of the two series does not necessarily exist. so