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Write the condition of continuity of a function f(x) at a point c in its domain. |
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Answer» A function f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied: (i) f(a) exists (i.e. the value of f(a) is finite) (ii) Limx→a f(x) exists (i.e. the right-hand limit = left-hand limit, and both are finite) (iii) Limx→a f(x) = f(a) The function f(x) is said to be continuous in the interval I = [x1,x2] if the three conditions mentioned above are satisfied for every point in the interval I. However, note that at the end-points of the interval I, we need not consider both the right-hand and the left-hand limits for the calculation of Limx→a f(x). For a = x1, only the right-hand limit need be considered, and for a = x2, only the left-hand limit needs to be considered. |
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