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4. Write the surface z = x² + y² in cylindrical coordinates (simplify its expression if possible). 2 5. Write the two-ply cone z² = x + y in spherical coordinates (simplify its expression if possible).

4. Write the surface z = x² + y² in cylindrical coordinates (simplify its expression if possible). 2 5. Write the two-ply cone z² = x + y in spherical coordinates (simplify its expression if possible).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 23E
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Needed to be solved Q4&Q5 correctly in 30 minutes and get the thumbs up please show neat and clean work for it By hand solution needed Please solve both question correctly
4. Write the surface z = x² + y² in cylindrical coordinates (simplify its expression if possible). 2 2 2 5. Write the two-ply cone z = x + y in spherical coordinates (simplify its expression if possible). 6. Let A and B be two open subsets of R". Show that their intersection An B is also an open set. 7. Let the function f: R² R defined as follows xy² + 2x²y x² + 4y² 0 f(x, y) = (a) Calculate the partial derivatives (b) Show that: af si (x, y) = (0,0) si (x, y) = (0,0). əx of f(x, y) -(0,0) = 0 et (c) Show with the definition & -ō that: and 3 (0, af ду af (x,y) ду (0,0) = 0. lim (x,y) →(0,0) has a point (x, y) not= (0, 0). f(x, y) = 0.
Transcribed Image Text:4. Write the surface z = x² + y² in cylindrical coordinates (simplify its expression if possible). 2 2 2 5. Write the two-ply cone z = x + y in spherical coordinates (simplify its expression if possible). 6. Let A and B be two open subsets of R". Show that their intersection An B is also an open set. 7. Let the function f: R² R defined as follows xy² + 2x²y x² + 4y² 0 f(x, y) = (a) Calculate the partial derivatives (b) Show that: af si (x, y) = (0,0) si (x, y) = (0,0). əx of f(x, y) -(0,0) = 0 et (c) Show with the definition & -ō that: and 3 (0, af ду af (x,y) ду (0,0) = 0. lim (x,y) →(0,0) has a point (x, y) not= (0, 0). f(x, y) = 0.
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