https://file.aiquickdraw.com/mathbot/file/1726863858712l97kwfgg.jpg

The limits for the given expressions are as follows:

- (a) \(\lim_{{x \to \infty}} (22x^2 - 15x^3) = -\infty\)
- (b) \(\lim_{{x \to -\infty}} (22x^2 - 15x^3) = \infty\)

Would you like more details on how these limits were computed or have any further questions?

Here are some related questions to explore:
1. How do you determine the behavior of polynomials at infinity?
2. What is the significance of the highest degree term in determining limits?
3. How does the sign of the leading coefficient affect the limit?
4. What methods can be used to analyze limits approaching infinity?
5. How would these limits change for a different polynomial function?

**Tip:** When evaluating limits for polynomial functions as \(x \to \infty\), focus on the term with the highest degree—it dominates the behavior of the function.

Evaluate the following limits: (a) lim(x→∞) (22x^2 - 15x^3), (b) lim(x→−∞) (22x^2 - 15x^3).

Learn how to evaluate limits of polynomial functions as x approaches infinity. This example walks through calculating lim(x→∞) (22x^2 - 15x^3) and lim(x→−∞) (22x^2 - 15x^3), focusing on the dominance of the highest degree term. Suitable for high school students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation