Determine Whether the Improper Integral $\int _ { 0 } ^ { \infty } x e ^ { - x / 3 } d x$

question 24

Multiple Choice

Determine whether the improper integral $\int _ { 0 } ^ { \infty } x e ^ { - x / 3 } d x$ diverges or converges. Evaluate the integral if it converges.

• A) 9
• B) \(e ^ { - 1 / 3 }\)
• C) \(- \frac { 1 } { 3 }\)
• D) 3
• E) diverges

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Definitions:

Dominant Strategy

In game theory, a strategy that is best for a player regardless of the strategies chosen by other players.

Individual Profits

The net gain in monetary terms realized by an individual or a single business entity from its investment or business operations.

Nash Equilibrium

A concept in game theory where no player can benefit by changing strategies if the strategies of the other players remain unchanged.

Oligopoly

A market structure characterized by a small number of firms controlling a large market share, leading to limited competition.