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2. Show that if vER is a vector and that a ER is a real number, then v^ (av) = 0

2. Show that if vER is a vector and that a ER is a real number, then v^ (av) = 0

Advanced Engineering Mathematics
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 NUM 2 needed Needed to be solved this question correctly in 30 minutes and get the thumbs up please show neat and clean work By hand solution needed
2. Show that if VER is a vector and that a ER is a real number, then vɅ (av) = 0 3. Consider the whole: π R = {(r₂0) |2 <r <3, 7/7 ≤ 05 Draw R in the (r, 0) plane, write R in Cartesian coordinates x = r cos 0, y = r sin 8, and draw R in the (x, y) plane. 2π 3 4. Write the surface z = x + y 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 + 2x² x² + 4y² 0 f(x, y) = si (x, y) = (0,0) si (x, y) = (0,0). af af (1)
Transcribed Image Text:2. Show that if VER is a vector and that a ER is a real number, then vɅ (av) = 0 3. Consider the whole: π R = {(r₂0) |2 <r <3, 7/7 ≤ 05 Draw R in the (r, 0) plane, write R in Cartesian coordinates x = r cos 0, y = r sin 8, and draw R in the (x, y) plane. 2π 3 4. Write the surface z = x + y 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 + 2x² x² + 4y² 0 f(x, y) = si (x, y) = (0,0) si (x, y) = (0,0). af af (1)
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