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University of El Paso 17 to pticuvin files\2Calculus Practice Problems $/28/2019 DEL #20. E is the solid region bounded by the ellipsoid t + y2 + 2 l. Do you consider E a simple solid region. Provide full explanation.

Answer 1

20. A region E is called a simple solid region if it simultaneously of type 1,2 and 3. E : x² + y + 7% = 1 Type 1 region can be written as a sx s6, h, (x) sysh (x). In xy plane x2 + y²21 1-1 So E is a ana yr, 1-X/ y . z 51-x/ Ji-x% sy { 1x/ type I region. Type 2 region can be written as csysd, 8. CY) <<< 8.09) similarly above, -1sYSI -√2 (1-42) < x < 2 (1-33 E is also type a region. Type 3 If a region is both type I and hype II, We call it type III. so E is also type 3 region. Just because solid. so of z-coordinate region become so we can call the region is a Simple solid