Continuity is an attribute of a function. Intuitively, a continuous function is a function in which the change of the input value is small enough and the change of the output is small enough. If a small change in the input value will cause a sudden jump, or even the output value is uncertain, the function is called a discontinuous function (or discontinuous function).

1 and the denominator cannot be 0, so x= 1 or x=2 is the breakpoint, which is divided into x.

2, logarithmic index is greater than zero, X.

3. The root number must be greater than or equal to 0, and 4≤x≤6 is a continuous interval.

4. arcsinx & gt0, and then the continuous interval is (0, π/2) starting from the domain [-π/2, π/2] of arcsinx.

Extended data:

Continuous function:

1. Definition of continuity: If the function f(x) is defined in x0 and the limit is equal to the function value, then the function is continuous in x0?

2. Sufficient condition: If the function f(x) is differentiable or differentiable at x0 (or stronger condition), then the function is continuous at x0.

3. Necessary condition: If the function f(x) is not defined at x0, or has no limit, or the limit is not equal to the function value, then it is discontinuous at x0?

4, observe the image (this is not rigorous, only for intuitive judgment)?

5. Remember the properties of some basic elementary functions. Most elementary functions are continuous within the definition domain?

6. Properties of continuous functions: The addition, subtraction, multiplication and composite functions of continuous functions are all continuous.

Baidu Encyclopedia-Continuity (Mathematical Noun)