# Concept of Continuity

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**1.Â Â Â Â (i) Right Hand Limit, **denoted by

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**Â Â Â Â Â Â Â Â Â Â Â Â Working Rule:**

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**Â Â Â Â Â Â Â Â Â Â Â Â **Replace x by (a + h) and take the limit as h Ã 0.

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Â Â Â Â Â Â Â **(ii)Â **Left Hand Limit, denoted by

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**Â Â Â Â Â Â Â Â Â Â Â Â Working Rule:**

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**Â Â Â Â Â Â Â Â Â Â Â Â **Replace x by (a â€“ h) and take the limit as h Ã 0.

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Â Â Â Â Â Â Â **(iii)Â Conclusion:**

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**Â Â Â Â Â Â Â Â Â Â Â Â **If f (a + 0) = f (a â€“ 0), then their common value is

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Â Â Â Â Â Â Â Â Â Â Â Â If f (a + 0) Â f (a â€“ 0), we say that Â does not exist.

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**2.Â Â Â Â Â Â Â **A function f (x) is said to be continuous at x = a, if

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Â Â Â Â i.e., f (a + 0) = f (a â€“ 0) = f (a)

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Â Â Â Â If f (x) is not continuous at x = a, we say that it is discontinuous at x = a

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