lista zadan nr 6.pdf

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lista_06.dvi
f(x, y) = 2x 3 −4y 7 + xy
p(x, y) =
2xy
x 2 +y 2
h(x, y, z) = arctg (x + y + z)−3(x 2 + y 2 + z 2 ) 3
h √
2 ,− √
f
u P
d(x, y) = sin(x cos y)
f(x, y) = 3x 3 −4xy + 2 u =
2
2
P = (1, 4)
2
f(x, y, z) = x + y 2 + z 3
u =
3 ,
3 ,
−2
3
P = (−3,−2,−1)
f(x, y) = x 2
u = [0, 1]
P = (10, 10)
f(x, y) = 1+y 2
sin x
x− p
f(x, y) = x y
f(x, y) =
y
f(x, y) = e e x + e e 2y
f(x, y, z) = (x + 1)(y + 2)(z + 3)
x R
F
cos x
R
F (x) =
xy dy
F (x) =
x 3 y dy
x
sin x
f(x, y) = (x−3) 2 + (y + 3) 4
f(x, y) =
p
4y−y 2 −x 2
f(x, y) = x sin y
f(x, y) = x 4 + y 3 + 32x−9y
f
f ′
y
f
x (x, y) = 6x + 4y
′
f
y (x, y) = 4x + 6y 2
′
f(1, 1) = 9
f ′
x (x, y) = 3x 2 + cos(xy) f ′
y (x, y) =−4y + y cos(xy)− y 2 sin(xy) f(0, 1) = 0
f ′
x (x, y) = 2x 3 + ln y
f ′
y (x, y) =
1
xy
f(1, 1) = 2
f(x, y) = xy + y 2 + x−y
f(x, y) = x 2 −2y 2
f(x, y) =
xy
x 2 +y 2 +1
f(x, y) = yx 2 + y 3 −4x 2
f(x, y) = e x sin y
f(x, y) = x 2 −6x cos y + 9
f
U
R 2
f(x, y) = x 2 + 2xy + 3y 2
U ={(x, y) :−2 6 x 6 4,−1 6 y 6 3}
f(x, y) = x 2 −4xy + y 3 + 4y U
(−1,−1) (7,−1) (7, 7)
f(x, y) = x 2 −2y 2
U ={(x, y) : x 2 + y 2 6 4}
f(x, y) = 4x 3 −2x 2 y + y 2
U
y = x 2 y = 9
f(x, y) = xy 3
(0, 0, 0)
P = (2, 1,−1)
4x−3y + z = 5
g(x, y) = x sin e x 2 +y 2
r(x, y, z) = x y z
i
1
2
p
x
f ′
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