Question

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Describe the long run behavior of f(x) = x³ = x³ + 3x5 +2
As x →→∞, f(x) → ? ✓
As x→∞, f(x) → ? ✓

Answer 1

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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