Let the limit of function f(x) in A be A, and the so-called local sign preservation of function limit is the sign of A, which can ensure that the sign of function f(x) itself is the same as the sign near A, so it is easy to prove the inequality between function and limit.

Sign preservation refers to the positive or negative property that the sign of a function satisfying certain conditions (such as the existence or continuity of limit) remains constant in a local range.

Extended data:

The limits of some functions are difficult or difficult to be obtained directly by limit algorithm, and need to be determined first. First, we should prove the convergence by monotone bounded theorem, and then find the limit value. 2. The key to applying the pinch theorem is to find functions with the same limit value, and when they meet the limit value, they tend to the same direction, thus proving or finding the limit value of the function.

The necessary and sufficient condition for the convergence of sequence is to give ε > 0, N(ε) exists, so when n >; n，m & gtn .

When the denominator is equal to zero, the trend value cannot be directly substituted into the denominator, which can be solved by the following small methods:

First: factorization, which makes the denominator not zero through simplification.

Second: If there is a root sign in the denominator, you can match a factor to remove the root sign.

Third: the solutions I mentioned above are all carried out under the condition that the trend value is fixed. If it tends to infinity, the numerator and denominator can be divided by the highest power of the independent variable. This theorem is usually used: the reciprocal of infinity is infinitesimal.

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