jee-main 2019 Q73

jee-main · India · session1_10jan_shift1 Sign Change & Interval Methods

For each $t \in R$, let $[ t ]$ be the greatest integer less than or equal to $t$. Then, $\lim _ { x \rightarrow 1 ^ { + } } \frac { ( 1 - | x | + \sin | 1 - x | ) \sin \left( [ 1 - x ] \frac { \pi } { 2 } \right) } { | 1 - x | [ 1 - x ] }$
(1) equals 0
(2) equals - 1
(3) does not exist
(4) equal 1

For each $t \in R$, let $[ t ]$ be the greatest integer less than or equal to $t$. Then, $\lim _ { x \rightarrow 1 ^ { + } } \frac { ( 1 - | x | + \sin | 1 - x | ) \sin \left( [ 1 - x ] \frac { \pi } { 2 } \right) } { | 1 - x | [ 1 - x ] }$\\
(1) equals 0\\
(2) equals - 1\\
(3) does not exist\\
(4) equal 1

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