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Question
`lim_(x -> 5) |x - 5|/(x - 5)` = ______.
Options
1
–1
Does not exist
None of these
MCQ
Fill in the Blanks
Solution
`lim_(x -> 5) |x - 5|/(x - 5)` = Does not exist.
Explanation:
`lim_(x -> 5) |x - 5|/(x - 5) = lim_(x -> 0) |5 - "h" - 5|/(5 - "h" - 5)` = –1
and `lim_(x -> 5^+) |x - 5|/(x - 5) = lim_("h" -> 0) |5 + "h" - 5|/(5 + "h" - 5)` = 1
Hence, limit does not exist.
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Concept of Limits
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