What is the definition of function continuity? How to judge whether a function is continuous?

If the limit of a function at point x is equal to the value of the function at that point, then the function is continuous at that point. If x is any point in the domain, then the function is continuous
It is OK to determine the continuous derivative of the function. If it can be derivative, it is sure to be continuous
It's better to understand the specific topic

RELATED INFORMATIONS

1. Continuity of piecewise function
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4. Given the function f (x) = | x | + 1, we study the continuity and differentiability of F (x) at x = 0
5. The differentiability and continuity of function f (x) = | cosx | are discussed
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7. The same Heine's theorem proves that cos (1 / x) = 1 does not exist when LIM (x tends to 0)
8. The absolute value of X-1 is divided by the limit of X-1
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12. The difference between the proof of continuity and uniform continuity of function
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14. The known function f (x) = 2Sin (AX - π / 6) sin (AX + π / 3)
15. Let f (x) = {x ^ 2, X ≤ 1; ax + B, x > 1} to make f (x) continuous and differentiable at x = 1, what values should a and B take?
16. Composite function f (x) = x ^ 2Sin (1 / x) (x > 0) f (x) = 0 x
17. Given the function f (x) = SiNx, x < and = 0, X is not equal to 0, x > 0, then f (0) =?
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20. Let f (x), X belong to R, X is not equal to 0, for any non-zero real number x, y, satisfy f (XY) = f (x) + F (y), find f (1), f (- 1)