1. The limit is infinite and easy to understand, which obviously violates the definition of limit existence.

2. Left and right limits are not equal, such as piecewise function.

3. There is no definite function value, such as lim(sinx) from 0 to infinity.

Existence or nonexistence conditions of limit:

1, if the result is infinitesimal, infinitesimal is replaced by 0, and 0 is also the limit.

2. If the limit of the numerator is infinitesimal, the limit of the denominator is not infinitesimal, the answer is 0, and the overall limit exists.

3. If the limit of the numerator is not infinitesimal and the limit of the denominator is infinitesimal, then the answer is either positive infinity or negative infinity, and the overall limit does not exist.

If the limits of numerator and denominator are infinitesimal, the final result must be determined by Robida method.

Function limit is one of the most basic concepts in higher mathematics, and the concepts such as derivative are all completed on the definition of function limit. Rational application of limit properties of functions. The common properties of function limit are uniqueness, local boundedness, order preservation, algorithm of function limit, composite function limit and so on.

Function limit can be divided into two parts, and the definition of ε-δ is more common in the proof of known limit value. Mastering this kind of proof is of great benefit to beginners to deeply understand the definition of application limit.

Take the limit of, for example, f(x) whose limit is at the point is defined as: for any given positive number ε (no matter how small it is), there is always a positive number, so that when X satisfies the inequality, the corresponding function value f(x) satisfies the inequality:, then when x→ x, the constant A is called the time limit of the function f(x).