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Find all points of discontinuity of f, where f is defined by:
f(x) = `{(x/|x|", if" x<0),(-1", if" x >= 0):}`
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f(x) = `{(x/|x|", if" x<0),(-1", if" x >= 0):}`
`lim_(x -> 0^-)` f(x) = `lim_(x -> 0^-) x/abs x`
= `lim_(x -> 0^-) x/(-x)`
= `lim_(x -> 0^-)` (−1)
= −1
`lim_(x -> 0^+)` f(x) = `lim_(x -> 0^+)` (−1) = −1
Also f(0) = −1
Thus, `lim_(x -> 0^-)` f(x) = `lim_(x -> 0^+)` f(x) = f(0)
Hence, f is continuous at x = 0.
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