## University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson

# Chapter 2 - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises - Page 109: 105

#### Answer

The graph is shown below. #### Work Step by Step

$$y=\frac{x}{\sqrt{4-x^2}}$$ The graph is shown below. From the formula, we takes note of two things: - First, the function is defined as $4-x^2\ge0$, which means $x^2\le4$, so $-2\le x\le 2$. Furthermore, $\sqrt{4-x^2}\ne0$, meaning that $x\ne\pm2$. The domain is limited to $(-2,2)$. We would expect the graph to range only in the small interval $(-2,2)$. This is definitely the case in the graph. The graph takes a curve from below to high above but only in the small interval $x\in(-2,2)$, not even touching $-2$ or $2$. - Second, as $x\to-2$ and $x\to2$, $\sqrt{4-x^2}$ both approaches $0$, meaning the function would approach $\pm\infty$ (in detail, $x\to-2$, $y\to-\infty$, and $x\to2$, $y\to\infty$). The graph would go from $-\infty$ near $x=-2$ to $\infty$ near $x=2$, meaning the graph must be narrow and change quite steeply on the way. This is the case as we look at the graph. After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.