Chapter 1: Limits
Section 1.5: Limits at Infinity and Infinite Limits
Graph fx=tanx on −3 π≤x≤3 π and determine all its asymptotes.
Figure 1.5.7(a) contains a graph of tanx and its vertical asymptotes that appear to be at x=2 k+12π, where k is an integer. Writing tanx as sinxcosx shows that the vertical asymptotes occur at the zeros of cosx, namely, at the odd half-multiples of π, that is, at:
…,−5 π2,−3 π2,−π2,π2,3 π2,5 π2,…
t1:=plot(tan(x),x=-3*Pi..3*Pi,y=-10..10,discont=true, color=green,tickmarks = [spacing((1/2)*Pi, 0), default]):
Figure 1.5.7(a) Graph of tanx (green) and its vertical asymptotes (red)
<< Previous Example Section 1.5
Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2021. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com
Download Help Document
What kind of issue would you like to report? (Optional)