If lim f (x) = a

Can be pushed

If f (x) >; =0 then lim f (x) = a >; =0

For example:

Let lim (x→ x0) f (x) = a.

If a is 0, the inference holds.

If A<0,

Then for-a/2 >; 0, has a centripetal neighborhood x0, which makes

| F(X)-A | & lt； -A/2，

Namely a/2

Then F.

Extended data:

When using the above two to find the function limit, we should pay special attention to the following points. 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.

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.

Baidu Encyclopedia-Function Limitation