Question

`lim_(x -> 5) |x - 5|/(x - 5)` = ______.

विकल्प

• 1

• –1

• Does not exist

• None of these

Answer 1

`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.