Math Problem Statement

Find the limit: lim(x→∞) [(4x^5 + 2x^4 + 6x^2 + 2x + 3) / (5x^5 + 2x^2 + x + 7)].

Solution

The given problem is:

lim⁡x→∞4x5+2x4+6x2+2x+35x5+2x2+x+7\lim_{x \to \infty} \frac{4x^5 + 2x^4 + 6x^2 + 2x + 3}{5x^5 + 2x^2 + x + 7}

Step-by-step solution:

  1. Identify the highest power of xx in the numerator and denominator:

    • The highest power in the numerator is x5x^5.
    • The highest power in the denominator is also x5x^5.

  2. **Divide every term in the

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Math Problem Analysis

Mathematical Concepts

Limits
Polynomial Division
Asymptotic Behavior

Formulas

For large x, the term with the highest power dominates in a polynomial.

Theorems

Limits of rational functions as x approaches infinity.

Suitable Grade Level

Grades 11-12

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