227 MATH OLD TEST 1 Note. This is served as an indication of the length and format of the test. Students are resposible for all materials that the actual test will cover. 1. "&:938>= Consider the surface whose equation is 4C oe B# % D# (a) Determine the equation of its trace on the BD-plane and name the trace.
(b) Determine the equation of its trace on the CD-plane and name the trace.
(c) Name its trace on planes parallel to the BC-plane.
(d) Name the surface and sketch it in a 3-dimentional coordinate system.
2. ':938>= Describe and name the surface whose equation is C# D# oe %; then sketch it.
3. &:938>= Sketch the region bounded by the surface= D oe B# C# and " Y D Y #
4. ):938>= Identify the following : (a) The surface whose equation in spherical coordinates 3 9 ) is 3 cos( 9) oe 2
(b) The surface whose equation in cylindrical coordinates < ) D is < # D# oe*
5. ):938>= (a) Write the spherical coordinates 3, ) , 9 of the point P whose rectangular coordinates are 1, $!
(b) Write the Cartesian equation of the surface 3# =38# 9-9= # ) - 9 = # 9oe"
6. (10 :938>= A particle moves with position function r > oe # ># i > j " Y > Y # Sketch the curve traced by particle, the the vector veclocity v" in the same picture.
r"#&r" !#&
and the
" 7. 20 :938>= Let r>oe $ >$ i ># j #> k be the position function of a particle. (a) Find the unit tangent vector T>
(b) Find the unit normal vector N>
(c) Find the normal component +R of the acceleration.
(d) Find the distance (arc length) that the particle travel= during 0 Y > Y $
8. ):938>= Suppose that v>oe=38> i -9=> j # > k and r ! oe # i j k. Find the position function r>
# 9. (a) %:938>= Evaluate '" " ># i %> $ j] dt
(b) (% :938>= Find gw > if g>oe " a , (># b -9=> c) >
10. (a) %:938>= A contour map for a function 0 is as shown. Estima...