Use set notation and spherical coordinates as in the equation F = {(0, 0, 0)| 0₁1 <0 <0₂₁ @1 << @2₁ 9(0₁) < p
Use set notation and spherical coordinates as in the equation F = {(0, 0, 0)| 0₁1 <0 <0₂₁ @1 << @2₁ 9(0₁) < p
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
![Use set notation and spherical coordinates as in the equation
\[ F = \{ (\rho, \theta, \varphi) \mid \theta_1 < \theta < \theta_2, \; \varphi_1 < \varphi < \varphi_2, \; g(\theta, \varphi) < \rho < h(\theta, \varphi) \} \]
to describe each region.
The region in the first octant that is below the cone \( z = \sqrt{3x^2 + 3y^2} \) and inside the cylinder \( x^2 + y^2 = 25 \).
\[ F = \left\{ (\rho, \theta, \varphi) \mid 0 < \theta < \boxed{\;} , \; \boxed{\;} < \varphi < \frac{\pi}{2}, \; 0 < \rho < \boxed{\;} \right\} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02af43a5-a1ff-44d9-89dd-1e2db9d95d08%2F38ffb371-6359-44da-ae09-93c9d01c2618%2Fp8k809g_processed.png&w=3840&q=75)
Transcribed Image Text:Use set notation and spherical coordinates as in the equation
\[ F = \{ (\rho, \theta, \varphi) \mid \theta_1 < \theta < \theta_2, \; \varphi_1 < \varphi < \varphi_2, \; g(\theta, \varphi) < \rho < h(\theta, \varphi) \} \]
to describe each region.
The region in the first octant that is below the cone \( z = \sqrt{3x^2 + 3y^2} \) and inside the cylinder \( x^2 + y^2 = 25 \).
\[ F = \left\{ (\rho, \theta, \varphi) \mid 0 < \theta < \boxed{\;} , \; \boxed{\;} < \varphi < \frac{\pi}{2}, \; 0 < \rho < \boxed{\;} \right\} \]
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