H.W.1
calculus 3
Exercise 1
Sketch the curve by eliminating the parameter, and indicate the direction of increasing
t.
x = 2t + 3, y = 4t − 5
x = sin t y = 2 cos t
Exercise 2
Find the slope of the tangent line on the following curve that correspond to t = 1.
x = t2 + 1 y = t3
Exercise 3
Find the length of the curve.
x = 2t,
y = t3/2 , 0 ≤ t ≤ 1
Exercise 4
Find the center and radius of the sphere that has
(1, −1, 1)
and
(0, 2, 3)
as endpoints
of a diameter
Exercise 5
Describe the surface whose equation is given by
Exercise 6
Find
u.v
and
Exercise 7
Let
u×v
u = (1, 2, 3)
where
and
u = (1, 3, 5),
v = (−1, 0, −2).
v on u.
x2 + z 2 + z 2 + 2x − 2y + 4z + 6 = 0
v = (2, −1, 3).
Find orthogonal projection of
orthogonal pro jection of
Exercise 8
Let
u = 2i − 3j + k,
v = 4i + j − 3k,
Find the volume of the parallelepiped generated by
1
w = j + 5k.
u, v, w
u
on
v
and