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Trong video này mình sẽ

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nói về các dạng gián đoạn

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mà chắc hẳn bạn đã gặp ở chương đại số rồi,

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hay tiền giải tích, nhưng giờ mình sẽ liên hệ thêm với

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giới hạn hai bên và giới hạn một bên.

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Vậy đầu tiên mình hãy xem qua cách phân loại gián đoạn.

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Vậy ở bên trái mình có đường cong này,

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nhìn như y bằng x bình,

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cho đến khi x bằng 3.

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Và thay vì nó bằng 3 bình,

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ở điểm này mình có khoảng trống,

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và hàm tại 3 được định nghĩa bằng 4.

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Và sau đó nó tiếp tục nhìn giống

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y bằng x bình trở lại.

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Cái này được biết đến như

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gián đoạn điểm, hay gián đoạn bỏ được.

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Và cũng dễ hiểu tại sao nó tên như vậy.

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Tại điểm đó mình không liên tục.

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Bạn có thể thử định nghĩa lại hàm

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cho nó liên tục tại điểm đó,

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nên gián đoạn này bỏ được.

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Nhưng vậy thì nó liên quan gì đến định nghĩa

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liên tục?

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Hãy nhớ lại định nghĩa của tính liên tục.

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Mình nói f liên tục.

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liên tục,

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khi và chỉ khi,

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hay để mình viết f liên tục

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tại x bằng c, khi và chỉ khi

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giới hạn khi x tiến đến c

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của f(x)

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