   Chapter 10.4, Problem 95E

Chapter
Section
Textbook Problem

Asymptote In Exercises 93-96, use a graphing utility to graph the equation and show that the given line is anasymptote of the graph.Name of Graph Polar Equation AsymptoteHyperbolic spiral r = 2 / θ y = 2

To determine

To Graph:

The graph of polar equation r=2θ by graphing utility andshow that given line y=2 is an asymptote of graph.

Explanation

Given:

Thegraph is Hyperbolic spiral And Polar equation r=2θ

The equation of asymptote y=1

Calculation:

The given equation of hyperbolic spiral is r=2θ

r as θ0

Since, the given polar equation r=2θθ=2r=2sinθrsinθ=2sinθy

y=2sinθθ

Take limit,

y=limθ0=2sinθθ

Apply L hospital rule, differentiation numerator and denominator

y=limθ0=2cosθ1<

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