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Set of all values of x such that lim(nra...

Set of all values of x such that `lim_(nrarroo) (1)/(1+((4tan^(-1)(2pix))/(pi))^(4n))` is non-zero and finite number when `n in N` is

A

`(0,(1)/(2pi))`

B

`(-(1)/(pi),(1)/(pi))`

C

`[-(1)/(2pi),(1)/(2pi)]`

D

`(-(1)/(2pi),0)`

Text Solution

Verified by Experts

The correct Answer is:
C
We must have
`" "-1le(4tan^(-1)(2pix))/(pi)le1`
`rArr" "-(pi)/(4)le tan^(-1)2pixle(pi)/(4)`
`rArr" "-1 le 2pixle 1`
`rArr" "x in[-(1)/(2pi),(1)/(2pi)]`
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CENGAGE-LIMITS-Single Correct Answer Type
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  10. lim(xrarroo) root3(x)(root3((x+1)^(2))-root3((x-1)^(2)))=

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  11. lim(nrarroo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

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  12. undersetlim(Xrarr2^(+)) {x}(sin(x-2))/((x-2)^(2))= (where {.} denotes ...

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  13. lim(xrarroo) (cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)}...

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