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lim(x to oo) (1-(4)/(x-1))^(3x-1) is eq...

`lim_(x to oo) (1-(4)/(x-1))^(3x-1)` is equal to

A

`e^(12)`

B

`e^(-12)`

C

`e^(4)`

D

`e^(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that , `underset(x to oo) ("lim") (1 - (4)/(x-1))^(3x - 1)`
`= underset(x to oo) ("lim") [ (1 - (4)/(x - 1))^(- ((x-1))/(4))]^(-4 ((3x - 1)/(x - 1)))`
`=e^(-4underset(xtooo)lim(3-(1)/(x))//(1-(1)/(x)))`
`implies^(-4xx3)=e^(-12)`
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