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Evaluate lim(x to oo) (log(3)3x)^(log(x)...

Evaluate `lim_(x to oo) (log_(3)3x)^(log_(x)3).`

A

e^(-1)

B

e

C

-1

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xtooo)lim(log_(3)3x)^(log_(x)3)=underset(xto1)lim(log_(3)+log_(3)x)^((1)/(log_(3)x))`
`=underset(xto1)lim(1+log_(3)x)^((1)/(log_(3)x))" "(1^(oo)"form")`
=e
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