Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - Concept Check: 6

Answer

(a) This function does not have any asymptotes. (b) This function does not have any asymptotes. (c) This function has vertical asymptotes for $x=(2m-1)\pi/2$ where $m$ is an integer. Here the function always goes to $+\infty$ from the left and to $-\infty$ to the right. (d) This function has two horizontal asymptotes: $y=\pi/2$ when $x$ goes to $+\infty$ and $y=-\pi/2$ when $x$ goes to $-\infty$. (e) This function has the horizontal asymptote $y=0$ when $x$ goes to $-\infty$. (f) This function has the vertical asymptote $x=0$ and it goes to $-\infty$ when $x$ approaches from the right. (g) This function has a vertical asymptote $x=0$ and a horizontal asymptote $y=0$. The function goes to $-\infty$ from the left and $+\infty$ from the right. (h) This function has no asymptotes.

Work Step by Step

(a) This function does not have any asymptotes. (b) This function does not have any asymptotes. (c) This function has vertical asymptotes for $x=(2m-1)\pi/2$ where $m$ is an integer. Here the function always goes to $+\infty$ from the left and to $-\infty$ to the right. (d) This function has two horizontal asymptotes: $y=\pi/2$ when $x$ goes to $+\infty$ and $y=-\pi/2$ when $x$ goes to $-\infty$. (e) This function has the horizontal asymptote $y=0$ when $x$ goes to $-\infty$. (f) This function has the vertical asymptote $x=0$ and it goes to $-\infty$ when $x$ approaches from the right. (g) This function has a vertical asymptote $x=0$ and a horizontal asymptote $y=0$. The function goes to $-\infty$ from the left and $+\infty$ from the right. (h) This function has no asymptotes.
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