Problem

Describe in words the region of $ \mathbb{R}^3 $ …

01:07

Problem 32 Hard Difficulty

Describe in words the region of $ \mathbb{R}^3 $ represented by the equation(s) or inequality.

$ x^2 + y^2 = 4 $

Answer

an infinite cylinder with radius 2 and the $z$ -axis as its axis.

Topics

Vectors

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Discussion

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Video Transcript

Okay, so we have an equation. X square plus was weeks poor. So Okay, this is the circle in art too. But what does it represent? Our three we're first in the jaw is graphene are too explain. See, the a reason O So the readers of the circles too, So happy we are to use this. So now with hidden in whoa recorded See what we can see That there's no Z in the equation. So the circle as a swear Rico's a square passwords for export It just a projection of the whole graft onto the ax or what? Plea. So now he is free the means we can too see freely from the whole room number. So finally, the regions or the graph of this equation after it's gonna be like a silent here. So it's like a Southerner and yes, we cutting If we cut it comes that under. In that parallel to ATS wise could be like a circle which is parallel. Two is production onto oh Wayne train. So, Ravi, the gravis will in this. But the length of it is infinite because you go through the whole rule number off the the White Z coordinates go through the whole room number. So this Salinger with even then this

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University of Illinois at Urbana-Champaign