Final answer:
The long run behavior of the function f(x) = x³ + 3x⁵ + 2 as x approaches infinity is that it increases without bound.
Step-by-step explanation:
The long run behavior of the function f(x) = x³ + 3x⁵ + 2 as x approaches infinity can be determined by looking at the degree of the highest power term in the function.
In this case, the highest power term is x⁵, which has a higher degree than x³. As x becomes larger and larger, the contribution of the x³ term becomes insignificant compared to the x⁵ term.
Therefore, as x approaches infinity, f(x) will be dominated by the x⁵ term, and the function will increase without bound.
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