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If 0ex1+xdx\int_{0}^{\infty} \frac{e^{-x}}{1+x} d x Converges, Find Its Value to 3 Decimal Places

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If 0ex1+xdx\int_{0}^{\infty} \frac{e^{-x}}{1+x} d x converges, find its value to 3 decimal places.Otherwise, enter "DNC".

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Definitions:

Utility Maximization

A principle in economics that suggests individuals and firms seek to allocate their resources in a way that maximizes their satisfaction or utility.

Diminishing Marginal Utility

A principle stating that as a person consumes more units of a particular good or service, the satisfaction (utility) gained from consuming each additional unit decreases.

Income Effect

Variations in income for either a person or the economy as a whole, and how these variations influence the demand for specific goods or services.

Substitution Effect

A shift in consumer preferences resulting from alterations in the comparative costs of different products, causing buyers to switch from one product to another.

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