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If lim(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n...

If `lim_(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2` where `"n" epsilonN` then the number of integers in the range of `x` is (a) 0 (b) 2 (c) 3 (d) 1

A

`0`

B

`2`

C

`3`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
D
`lim_(nrarroo) 1/(((3x-4)/2)^(n)+2+1/n)=1/2`
`implies-1lt(3x-4)/2lt1implies-2lt3x-4lt2`
`2lt3xlt6=2/3ltxlt2`
Only one integer `x=1`
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