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5 Pages

### old_t12

Course: MA 227, Fall 2009
School: Alabama
Rating:

Word Count: 373

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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. &quot;&amp;:938&gt;= 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....

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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...

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