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 dx si (x, y) = (0,0) si (x, y) = (0,0). af Əx (0,0) = 0 et 8 Let the function f R² (c) Show with the definition & - ō that: (x, y) ду and R be defined by af ду -(x, y) ,0) = 0. lim (x,y) →(0,0) has a point (x, y) not= (0, 0). f(x, y) = 0.
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 dx si (x, y) = (0,0) si (x, y) = (0,0). af Əx (0,0) = 0 et 8 Let the function f R² (c) Show with the definition & - ō that: (x, y) ду and R be defined by af ду -(x, y) ,0) = 0. lim (x,y) →(0,0) has a point (x, y) not= (0, 0). f(x, y) = 0.
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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Needed to be solved Q6 Correctly in 30 minutes and get the thumbs up please show neat and clean work for it
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By hand solution needed
Transcribed Image Text:6. Let A and B be two open subsets of R". Show that their intersection An B is also an open
set.
2
7. Let the function f : R
f(x, y): =
(b) Show that:
xy² + 2x²y
zy
x² + 4y²
0
f(x, y)
(a) Calculate the partial derivatives
af
Əx
{
8. Let the function f : R²
R defined as follows
si
x² + y²
0
si
(c) Show with the definition & - ō that:
(y + 2x²)²
lim
Show that (x,y) (0,0)
(0,0) = 0 et
(x, y) = (0,0)
(x, y) = (0,0).
af
(x, y)
af
ду
f (x, y)
R be defined by
and
af
-(x, y)
ду
(0,0) = 0.
lim
(x,y) →(0,0)
si (x, y) = (0,0)
si (x, y) = (0,0).
does not exist.
has a point (x, y) not= (0, 0).
f(x, y) = 0.
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