Question

problem 15
$lim_{x \to infty} -4x^8 + 7x^3 - 5$

Explanation:

Step1: Identify dominant term

For polynomials as $x\to\infty$, the highest-degree term dominates. Here, the highest degree term is $-4x^8$.

Step2: Evaluate limit of dominant term

As $x\to\infty$, $x^8\to\infty$, so $-4x^8\to -\infty$. The lower-degree terms ($7x^3$ and $-5$) become negligible compared to $-4x^8$.

Answer:

$-\infty$