13.5 Triple Integrals in Cylindrical and Spherical Coordinates Problem 35 ### 35–38. Sets in Spherical Coordinates**Task:** Identify and sketch the following sets in spherical coordinates.Understanding spherical coordinates is essential as they provide a different perspective from Cartesian coordinates, particularly useful in three-dimensional space. A point in spherical coordinates is represented by three parameters: $ \rho $ (the radial distance from the origin), $ \theta $ (the polar angle from the positive Z-axis), and $ \phi $ (the azimuthal angle in the XY-plane from the positive X-axis).In this exercise, you are tasked to:- **Identify:** Analyze the given mathematical descriptions or equations of sets and determine their nature (such as spheres, cones, or other surfaces).- **Sketch:** Create graphical representations of the sets using the spherical coordinate framework.This practice enhances spatial reasoning and a deeper understanding of geometric transformations and their applications in physics, engineering, and computer graphics. The expression is from a mathematical context, likely related to spherical coordinates. Here is the transcription:**35. \{($\rho$, $\varphi$, $\theta$) : $1 \leq \rho \leq 3$\}**This set describes a region in three-dimensional space using spherical coordinates. It specifies that the radial distance $\rho$ ranges from 1 to 3 units. No restrictions are given for the angles $\varphi$ (polar angle) and $\theta$ (azimuthal angle), implying they can take any value within their typical ranges: $0 \leq \varphi \leq \pi$ and $0 \leq \theta < 2\pi$. This represents a spherical shell or annulus in 3D space centered at the origin, with inner radius 1 and outer radius 3.

Given:The spherical coordinates are being set as

Answered: 35. { (р, ф, 0): 1

Math

Advanced Math

35. { (р, ф, 0): 1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

13.5 Triple Integrals in Cylindrical and Spherical Coordinates Problem 35

### 35–38. Sets in Spherical Coordinates

**Task:** Identify and sketch the following sets in spherical coordinates.

Understanding spherical coordinates is essential as they provide a different perspective from Cartesian coordinates, particularly useful in three-dimensional space. A point in spherical coordinates is represented by three parameters: $ \rho $ (the radial distance from the origin), $ \theta $ (the polar angle from the positive Z-axis), and $ \phi $ (the azimuthal angle in the XY-plane from the positive X-axis).

In this exercise, you are tasked to:
- **Identify:** Analyze the given mathematical descriptions or equations of sets and determine their nature (such as spheres, cones, or other surfaces).
- **Sketch:** Create graphical representations of the sets using the spherical coordinate framework.

This practice enhances spatial reasoning and a deeper understanding of geometric transformations and their applications in physics, engineering, and computer graphics.

The expression is from a mathematical context, likely related to spherical coordinates. Here is the transcription:

**35. \{($\rho$, $\varphi$, $\theta$) : $1 \leq \rho \leq 3$\}**

This set describes a region in three-dimensional space using spherical coordinates. It specifies that the radial distance $\rho$ ranges from 1 to 3 units. No restrictions are given for the angles $\varphi$ (polar angle) and $\theta$ (azimuthal angle), implying they can take any value within their typical ranges: $0 \leq \varphi \leq \pi$ and $0 \leq \theta < 2\pi$. This represents a spherical shell or annulus in 3D space centered at the origin, with inner radius 1 and outer radius 3.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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