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Question
Find all points of discontinuity of f, where f is defined by `f (x) = {(x/|x|, if x<0),(-1, if x >= 0):}`
Solution
`f (x) = {(x/|x|, if x<0),(-1, if x >= 0):}`
`lim_(x -> 0^-) f(x) = lim_(x -> 0^-) x/abs x`
= `lim_(h -> 0) ((0 - h))/ abs (0 - h)`
`= lim_(h -> 0) (-h)/h = - 1`
`lim_(x -> 0^+)` f(x) = -1
f(0) = - 1
Hence, f is continuous at x = 0.
There are no points of discontinuity here.
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