Hw 5 Due Mar 8
2.5 Exercise: 11, 13, 28, 30, 36, 37, 39, 41
2.6 Exercise: 2, 10, 14, 22, 25, 49.
Suppose the parameterized curve
y = y(x)
is given implicitly by (as the intersection of two
z = z(x)
surfaces)
3x2 + 4xy 5zex1 = 0
2x2 + y = 0
Find the tan
1. Chain Rule: Given G(s, t) = F(H(s, t), or G = F H, where F = F(x, y, z), and
H = H(s, t), then the chain rule tells us, at the point (s0 , t0 ), if (x0 , y0 , z0 ) = H(s0 , t0 ),
then
DG(s0 , t0 ) = DF(x0 , y0 , z0 )DH(s0 , t0 ),
2. Given region D = (x
Hw 4 Due Feb 22
2.2 Exercise 7,8,10,12,15,18,28,35,36,46
2.3 Exercise 3,11,39,40,47(b)
2.4 Exercise 6,7
Use both the direct method and product rule to calculate
where f (x, y, z) = 3x, g(x, y, z) =
D(f g)
x
1 2 3
y . Do the two methods give the same