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प्रश्न
Is the function defined by `f(x) = {(x+5, if x <= 1),(x -5, if x > 1):}` a continuous function?
उत्तर
`f (x) = {(x+5, if x<=1),(x - 5, if x > 1):}`
`lim_(x -> 1^-) f(x) = lim_(x -> 1^-)` (x + 5)
= `lim_(h -> 0)` [1 - h + 5]
= `lim_(h -> 0)` (6 - h)
= 6 - 0
= 6
`lim_(x -> 1^+) f(x) = lim_(x -> 1^+)` (x - 5)
= `lim_(h -> 0)` (1 + h - 5)
= `lim_(h -> 0)` (h - 4)
= 0 - 4
= - 4
Hence, f is not continuous at x = 1.
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