No matter how small, there is always a positive number.
So when x satisfies the inequality,
, the corresponding function values f(x) all satisfy the inequality.
Then the constant a is called the function f(x), when
Time limit, recorded as
Extended data
Four Algorithms of Function Limit
Assuming that f(x) and g(x) exist in the same independent variable process, their limits of sum, difference, product and quotient (the function as denominator and its limit value are not equal to 0) also exist, and the limit value is equal to the sum, difference, product and quotient of the limits. Multiplying a non-zero constant by a function does not change the existence of function limits.
Related theorem: pinch theorem
Let L(x), f(x) and R(x) satisfy L(x)≤f(x)≤R(x) in an eccentric neighborhood or infinite neighborhood during the process of independent variable change, and the limits of L(x) and R(x) exist and are equal during the process of independent variable change, then the limit of f(x) is also in the process of independent variable change.