If f is differentiable at a point x, then f must also be continuous at x. In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable.
Continuity implies integrability; if some function f(x) is continuous on some interval [a,b], then the definite integral from a to b exists. While all continuous functions are integrable, not all integrable functions are continuous.
所以簡單d講任何d到既function=>continuous=>in到,但相反in到既function唔一定係continuous=>唔一定d到
想了解多d可以讀下Analysis
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