NIMCET 2014 Question Paper with solutions

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Question : 38 of 120

Marks: +1, -0

If f (x) =

\{\table {sin[x]}/[x] , [x] ≠ 0 ;0 , [x] = 0

, where [x] is the largest integer but not larger than x , then

{\lim}↙{x→0}

f (x) is

- 1
0
1
Does not exist

Solution:

f (x) =

\{\table {sin(-1)}/{-1} = sin,\when -1 < ≤ x < 0 ; 0 , \when 0 ≤ x < 1

⇒

\lim↙{x→0^{-}}

f (x) = sin 1 and

\lim_{x→0^{\+}

f (x) = 0
∴ LHS ≠ RHS
So, limit does not exist

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