7677 Vertical and horizontal asymptotes of polar curvescan sometimes be detected by
Chapter 10, Problem 76(choose chapter or problem)
Vertical and horizontal asymptotes of polar curves can sometimes be detected by investigating the behavior of \(x=r \cos \theta\) and \(y=r \sin \theta\) as \(\theta\) varies. This idea is used in these exercises.
Show that the hyperbolic spiral \(r=1 / \theta(\theta>0)\) has a horizontal asymptote at \(y=1\) by showing that \(y \rightarrow 1\) and \(x \rightarrow+\infty\) as \(\theta \rightarrow 0^{+}\). Confirm this result by generating the spiral with a graphing utility.
Equation Transcription:
Text Transcription:
x=r cos theta
y=r sin theta
theta
r=1/theta(theta>0)
y=1
y rightarrow 1
x rightarrow +infty
Theta rightarrow 0^+
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer