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Let [x] denote the greatest integer not ...

Let [x] denote the greatest integer not exceeding x. If `l_(1) = lim_(x rarr 2^(+)) (x^(2) + [x]), l_(2) = lim_(x rarr 2^(+)) (2x - [x])` and `l_(3) = lim_(x rarr (pi)/(2))((cos x)/(x-(pi)/(2)))`, then

A

`l_(2) lt l_(3) lt l_(1)`

B

`l_(1) lt l_(3) lt l_(2)`

C

`l_(1) lt l_(2) lt l_(3)`

D

`l_(3) lt l_(2) lt l_(1)`

Text Solution

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The correct Answer is:
D
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