(0, 0) a a > 0
y = 0
[0, 1] t (et cos t, et sin t, et)
a a > 0
b b > 0
 Åš
2
x2+y2-x
Åš(x, y) = (x +y2-y , ) R2 \ {(0, 0)}
x2+y2 x2+y2
Åš(x, y, z) = (x, y, z) R3
Åš(x, y, z) = (x4y3, x3y4, z) R3
F
“
F (x, y) = (cos(4y), -4x sin(4y)) “
Ä„ Ä„
A = (1, ) B = (2, )
6 4
x -y
F (x, y) = ((x-y) , ) “
2
(x-y)2
A = (0, -1) B = (1, 0) y < x
"
1
F (x, y) = (x3 cos2(5x) + x3 + 4y, -6x + y sin(y )) “
A = (2, 1) B = (6, 1) C = (6, 3) D = (2, 3)
F (x, y) = (x2y2 + y, x3y + x) “ x2 + y2 = 2x
x dx - y dz “ x +
“
y + z = 3 x2 + 4y2 = 4
z = 0 -2Ä„
x
"dx+y dy “ b2x2 + a2y2 = a2b2
1+x2+y2
“
a, b > 0
F “
F (x, y, z) = (xy, z + y, z) “
Ä„
A = (0, 2, ) B = (2, 0, 0)
2
y2
F (x, y) = (x+1, 2y ln(x + 1) + 1) “ x2 + y2 = 1 A = (-1, 0)
B = (1, 0)