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Question
Show that `lim_(x -> 4) |x - 4|/(x - 4)` does not exists
Solution
Given `lim_(x -> 4) |x - 4|/(x - 4)`
L.H.L. = `lim_(x -> 4^-) (-(x - 4))/(x - 4) = - 1` ......`[because |x - 4| = -(x - 4) "if" x < 4]`
R.H.L. = `lim_(x -> 4^+) (x - 4)/(x - 4)` = 1 ......`[because |x - 4| = (x - 4) "if" x > 4]`
Since L.H.L. ≠ R.H.L.
Hence, the limit does not exist.
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