   Chapter 15.8, Problem 14E

Chapter
Section
Textbook Problem

Sketch the solid described by the given inequalities.14. ρ ≤ 2, ρ ≤ csc ϕ

To determine

To sketch: The solid described by the given inequalities.

Explanation

Given:

The inequality ρ2,ρcscϕ .

The given equations becomes,

ρ=2x2+y2+z2=2x2+y2+z2=4

And,

ρ=cscϕρ(1cscϕ)=1ρsinϕ=1

Thus, the value of x2+y2 is,

x2+y2=(ρsinϕcosθ)2+(ρsinϕsinθ)2=ρ

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