determine the oblique asymptote of the graph of the function. f(x) = (10x^5 - 2)/(5x^4 - 1) the oblique…

determine the oblique asymptote of the graph of the function. f(x) = (10x^5 - 2)/(5x^4 - 1) the oblique asymptote is y =

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:

$y = 2x$