Final Answer:
The limit of x raised to the power of any positive constant (xʳ) as x approaches infinity is infinity.
Step-by-step explanation:
When evaluating the limit lim (xʳ) as x approaches infinity, the behavior depends on the value of the exponent r. If r is a positive constant, the function grows without bound as x becomes larger. Mathematically, it can be expressed as:
lim (xʳ) as x → ∞ = ∞
This result signifies that the function xʳ becomes unbounded as x approaches infinity, indicating exponential growth. Understanding the behavior of functions as x approaches infinity is crucial in calculus and mathematical analysis.
In practical terms, this scenario often represents situations where a quantity increases rapidly without a bound as the variable (x in this case) becomes larger. It is a fundamental concept in calculus and helps analyze the growth rates of various functions in different mathematical contexts.