Cylinders in ℝ^3 Consider the following cylinders in ℝ^3. a. Identify the coordinate axis to whi

Name: Problem 7, Chapter 13: Calculus: Early Transcendentals
Uploaded: 2020-06-26T18:39:02-08:00
Duration: 2 min 15 s
Channel: Jeffrey Utley
Description: Cylinders in ℝ^3 Consider the following cylinders in ℝ^3. a. Identify the coordinate axis to which the cylinder is parallel. b. Sketch the cylinder. z=y^2

step 1 question gives us a specific 3D equation and then it asks us to find the coordinate access for w

Question

Cylinders in $\mathbb{R}^{3}$ Consider the following cylinders in $\mathbb{R}^{3}$. a. Identify the coordinate axis to which the cylinder is parallel. b. Sketch the cylinder. $$z=y^{2}$$

   Cylinders in $\mathbb{R}^{3}$ Consider the following cylinders in $\mathbb{R}^{3}$.
a. Identify the coordinate axis to which the cylinder is parallel.
b. Sketch the cylinder.
$$z=y^{2}$$

Calculus: Early Transcendentals

William Briggs, Lyle… 3rd Edition

Chapter 13, Problem 7

Instant Answer

Solved by Expert Jeffrey Utley

06/26/2020

Step 1

In this equation, the variable $x$ is not present. This means that the value of $z$ does not change as $x$ changes. Therefore, the cylinder is parallel to the $x$-axis. Show more…

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Cylinders in $\mathbb{R}^{3}$ Consider the following cylinders in $\mathbb{R}^{3}$. a. Identify the coordinate axis to which the cylinder is parallel. b. Sketch the cylinder. $$z=y^{2}$$

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Key Concepts

Cylinder in ?³

A cylinder in three-dimensional space is a surface obtained by translating a curve along a line, known as the axis of the cylinder. In such surfaces, one coordinate is free and does not affect the defining equation of the curve, resulting in uniform cross-sections parallel to a plane perpendicular to the axis.

Parabolic Cylinder

A parabolic cylinder is a type of cylinder where the generating plane curve is a parabola. In the equation z = y², the relation between y and z forms a parabola in the y-z plane, and because x does not appear in the equation, it indicates that the surface is extended infinitely in the x direction, making the x-axis the axis of translation.

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