Confirm that ϕ is a potential function for F(r) on some region, and state the region. a ϕ ( x , y ) = 2 y 2 + 3 x 2 y − x y 3 F( x , y ) = ( 6 x y − y 3 ) i + ( 4 y + 3 x 2 − 3 x y 2 ) j b ϕ ( x , y , z ) = x sin z + y sin x + z sin y F( x , y , z ) = ( sin z + y cos x ) i + ( sin x + z cos y ) j + ( sin y + x cos z ) k
Confirm that ϕ is a potential function for F(r) on some region, and state the region. a ϕ ( x , y ) = 2 y 2 + 3 x 2 y − x y 3 F( x , y ) = ( 6 x y − y 3 ) i + ( 4 y + 3 x 2 − 3 x y 2 ) j b ϕ ( x , y , z ) = x sin z + y sin x + z sin y F( x , y , z ) = ( sin z + y cos x ) i + ( sin x + z cos y ) j + ( sin y + x cos z ) k
Confirm that
ϕ
is a potential function for
F(r)
on some region, and state the region.
a
ϕ
(
x
,
y
)
=
2
y
2
+
3
x
2
y
−
x
y
3
F(
x
,
y
)
=
(
6
x
y
−
y
3
)
i
+
(
4
y
+
3
x
2
−
3
x
y
2
)
j
b
ϕ
(
x
,
y
,
z
)
=
x
sin
z
+
y
sin
x
+
z
sin
y
F(
x
,
y
,
z
)
=
(
sin
z
+
y
cos
x
)
i
+
(
sin
x
+
z
cos
y
)
j
+
(
sin
y
+
x
cos
z
)
k
Caitulu.
Find the integration of the function
f(u) = u(u+ 4) + u-4 + /(u+5)+ (u+4)
%3D
no
VIva
u = 2-x. f wz-xdx=
If U = 2–x,
Suppose that f(x, y) = -2z4+3 zy2 + 3y2, z=rcos (t) and y=rsin(t). Find
af af
and (write your answers as functions of the pair r and t).
Ot
Or
af
Or
af
ICH
Chapter 15 Solutions
Calculus Early Transcendentals, Binder Ready Version
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