lim (x→∞) (5x³ - 9x⁵)/(3x⁸ + 4x³ - 8) =

Question

Accepted Answer

# Explanation:
## Step1: Identify the highest degree term
In the numerator $5x^3 - 9x^5$, the highest degree term is $-9x^5$ (degree 5). In the denominator $3x^8 + 4x^3 - 8$, the highest degree term is $3x^8$ (degree 8).

## Step2: Divide numerator and denominator by the highest degree term in the denominator
Divide each term in the numerator and denominator by $x^8$:
$$
\begin{align*}
\lim_{x \to \infty} \frac{\frac{5x^3}{x^8} - \frac{9x^5}{x^8}}{\frac{3x^8}{x^8} + \frac{4x^3}{x^8} - \frac{8}{x^8}}&=\lim_{x \to \infty} \frac{\frac{5}{x^5} - \frac{9}{x^3}}{3 + \frac{4}{x^5} - \frac{8}{x^8}}
\end{align*}
$$

## Step3: Evaluate the limit as $x \to \infty$
As $x \to \infty$, terms with $x$ in the denominator ($\frac{5}{x^5}$, $\frac{9}{x^3}$, $\frac{4}{x^5}$, $\frac{8}{x^8}$) approach 0. So we substitute these limits:
$$
\frac{0 - 0}{3 + 0 - 0}=\frac{0}{3} = 0
$$

# Answer:
$0$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the highest degree term

Step2: Divide numerator and denominator by the highest degree term in the denominator

Step3: Evaluate the limit as \(x \to \infty\)

Answer: