((2x-y2) Let f(x, y) = x² + y² (x, y) = (0,0) 2, (x, y) = (0,0) Are fx and fy continuous at (0,0)? Is lim (Ax,Ay)→(0,0) ƒ(a+ªx,b+ªy)—ƒ(a,b)—ƒx(a,b)^x-fy(a,b)▴y (Ax)²+(Ay)² = 0?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Differentiability of f(x,y). [Part 2]

(2x-y²)²
x2+y*
2,
(x, y) # (0,0)
Let f(x, y) =
(х, у) %3D (0,0)
I.
Are f, and f, continuous at (0,0)?
Is
lim
(Ax,Ay)¬(0,0)
f(a+Ax,b+Ay)-f (a,b)-fx(a,b)Ax-fy(a,b)Ay
V(Ax)2+(Ay)²
I.
0?
Transcribed Image Text:(2x-y²)² x2+y* 2, (x, y) # (0,0) Let f(x, y) = (х, у) %3D (0,0) I. Are f, and f, continuous at (0,0)? Is lim (Ax,Ay)¬(0,0) f(a+Ax,b+Ay)-f (a,b)-fx(a,b)Ax-fy(a,b)Ay V(Ax)2+(Ay)² I. 0?
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