_ x 3 ,[x] = , (where [.] = greatest integer function) - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 3} \,[x] = $, (where $[.] =$ greatest integer function)

A
$2$
B
$3$
✓
Does not exist
D
None of these

✓

Answer

Correct option: C.

Does not exist

c
(c) $\mathop {\lim }\limits_{h \to {0^ + }} \,[3 + h] = 3$ and $\mathop {\lim }\limits_{h \to {0^ - }} \,[3 - h] = 2$

$\therefore$ $\mathop {\lim }\limits_{x \to 3} \,\,[x]$ does not exist.

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