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प्रश्न
Discuss the continuity of the function f, where f is defined by:
f(x) = `{(3", if" 0 <= x <= 1),(4", if" 1 < x < 3),(5", if" 3 <= x <= 10):}`
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उत्तर
f(x) = `{(3", if" 0 <= x <= 1),(4", if" 1 < x < 3),(5", if" 3 <= x <= 10):}`
For 0 ≤ x ≤ 1, f(x) = 3;
1 < x < 3, f(x) = 4 and
3 ≤ x ≤ 10, f(x) = 5, is a continuous function.
So this is a function.
At x = 1,
`lim_(x -> 1^-)` f(x) = `lim_(x -> 1^-)` (3) = 3
`lim_(x -> 1^+)` f(x) = `lim_(x -> 1^+)` (4) = 4
Hence, f is not continuous at x = 1.
At x = 3,
`lim_(x -> 3^-)` f(x) = `lim_(x -> 3^-)` (4) = 4
`lim_(x -> 3^+)` f(x) = `lim_(x -> 3^+)` (5) = 5
Hence, f is not continuous at x = 3.
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