Q1. Determine for .

Background

Topic: Limits and End Behavior of Polynomial Functions

This question tests your understanding of how to analyze the end behavior of a polynomial function as approaches positive infinity. Recognizing which term dominates as $x$ becomes very large is key in such problems.

Key Terms and Formulas

• Limit at Infinity: describes the value that approaches as increases without bound.

• Dominant Term: For polynomials, the term with the highest degree in will dominate the behavior as .

Step-by-Step Guidance

1. Identify the degree of each term in . The highest degree term is .

2. As , compare the growth rates of , , and the constant $1x^3x for large $x$.

3. To formalize this, factor from each term to rewrite as .

4. Analyze the behavior of the expression inside the parentheses as .

Try solving on your own before revealing the answer!