The term "distinguished limit" can refer to different concepts depending on the context, particularly in mathematics or analysis. However, it is not a widely recognized or standard term in mathematical literature. It's possible that you might be referring to one of the following ideas: 1. **Limit in Analysis**: In mathematical analysis, the limit of a function or sequence describes the value that it approaches as the input or index approaches some point.

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A distinguished limit rescales variables so that two or more effects enter the leading asymptotic balance together. It identifies a region whose governing equation differs from the equations in adjacent scales.