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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

l exists but m does not

B

m exists but l does not

C

both l and m exist

D

neither l nor m exists

Text Solution

Verified by Experts

The correct Answer is:
`e`
`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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