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The value of Lim(ntooo) ((2x)/(pi)cot^(-...

The value of `Lim_(ntooo) ((2x)/(pi)cot^(-1)(nx)-x)` is/are

A

`1,xgt0`

B

`x,xlt0`

C

`-x,xgt0`

D

`-1,xlt0`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(ntooo)Lim(2x)/(pi)((pi)/(2)-tan^(-1)nx)-x`
`underset(ntooo)Limx-(2x)/(pi)tan^(-1)nx-x`
`underset(ntooo)Lim-(2x)/(pi)tan^(-1)nx={{:(0,"if",x=0),(-x,"if",xgt0),(x,"if",xlt0):}`
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