determine the oblique asymptote of the graph ...
determine the oblique asymptote of the graph of the function. f(x) = (10x^5 - 2)/(5x^4 - 1) the oblique asymptote is y =
Answer
# Explanation:
## Step1: Perform polynomial long - division
Divide $10x^{5}-2$ by $5x^{4}-1$.
\[
\begin{align*}
\frac{10x^{5}-2}{5x^{4}-1}&=\frac{10x^{5}- 2x}{5x^{4}-1}+\frac{2x - 2}{5x^{4}-1}\\
& = 2x+\frac{2x - 2}{5x^{4}-1}
\end{align*}
\]
As $x\to\pm\infty$, $\lim_{x\to\pm\infty}\frac{2x - 2}{5x^{4}-1}=0$.
# Answer:
$y = 2x$