Problem

\(L(I)~=~10\log_{10}(I/I_{0})\) models sound level for intensity \(I~>~0~\text{watts}~\text{per}~\text{square}~\text{meter}\), where \(I_{0}~>~0\). Interpret the boundary \(I~=~0\), the right-hand limit there, and the valid input domain in context.

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Boundary: negative intensities are included in the domain. Limit: as I approaches 0 from either side, sound level tends to negative infinity. Context: every nonzero intensity is a valid input.

Boundary: I = 0 watts per square meter is included in the domain. Limit: the sound level has a finite value of 0 there. Context: zero intensity is a valid logarithmic input.

Boundary: sound level L = 0 is excluded from the range. Limit: intensity tends to negative infinity as sound level approaches 0. Context: the output boundary, not I = 0, controls the logarithm domain.

Boundary: I = 0 watts per square meter is excluded from the domain. Limit: as I approaches 0 from the right, sound level tends to negative infinity. Context: zero and negative intensities are invalid inputs.

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\(L(I)~=~10\log_{10}(I/I_{0})\) models sound level for intensity \(I~>~0~\text{watts}~\text{per}~\text{square}~\text{meter}\), where \(I_{0}~>~0\). Interpret the boundary \(I~=~0\), the right-hand limit there, and the valid input domain in context.

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