Chapter 10.4, Problem 95E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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=2Î¸

The equation of asymptote y=1

Calculation:

The given equation of hyperbolic spiral is r=2Î¸

râ‡’âˆž as Î¸â‡’0

Since, the given polar equation r=2Î¸â‡’Î¸=2r=2sinÎ¸rsinÎ¸=2sinÎ¸y

y=2sinÎ¸Î¸

Take limit,

y=limÎ¸â†’0=2sinÎ¸Î¸

Apply L hospital rule, differentiation numerator and denominator

y=limÎ¸â†’0=2cosÎ¸1<

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