## Calculus: Early Transcendentals 8th Edition

(a) These two functions seem to have the same end behavior. (b) Since the ratio of $\frac{P(x)}{Q(x)}$ approaches 1 as $~~x \to \infty~~$, $P$ and $Q$ have the same end behavior.
(a) When we view the graphs in the viewing rectangle $[-2,2]$ by $[-2,2]$, the graphs have a general trend that is similar, but the details are somewhat different. When we view the graphs in the viewing rectangle $[-10,10]$ by $[-10,000,10,000]$, the graphs have a very similar shape. These two functions seem to have the same end behavior. (b) $\lim\limits_{x \to \infty}\frac{P(x)}{Q(x)}$ $=\lim\limits_{x \to \infty}\frac{3x^5-5x^3+2x}{3x^5}$ $=\lim\limits_{x \to \infty}\frac{3x^5/x^5-5x^3/x^5+2x/x^5}{3x^5/x^5}$ $= \frac{3}{3}$ $= 1$ Since the ratio of $\frac{P(x)}{Q(x)}$ approaches 1 as $~~x \to \infty,~~$ $P$ and $Q$ have the same end behavior.