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Evaluate the limit lim_(x→∞) ((3x-4)/(3x+2))^((x+1)/(3)):

1. e^(-1/3)
2. e^(-2/3)
3. e⁻¹
4. e⁻²

Correct answer: e^(-2/3)

Solution

Write (3x-4)/(3x+2)=1-6/(3x+2). The limit is exp(lim ((x+1)/3)*(-6/(3x+2))) = exp(-6/(3*3)) = exp(-2/3).

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