Fall 2003 Prelim 2 - MATH 192 FALL 2003 PRELIM 2 No...

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Unformatted text preview: MATH 192, FALL 2003 PRELIM 2 No calculators. An 8.5 x 11 in. sheet of paper with information on both sides is allowed. Please make sure to give adequate reasons for all your answers. 1. (10 points) Find equati0n(s) for the line L going through the points P(0, 1, 0) and Q(2, 3, 4). 2. (10 points) Consider the lines L1 : x = 2 + t, y = 2 + 3t, 2 2 4t and L2: $=6+2s, y=4+s, zzO. a) Find the coordinates of the point of intersection of L1 and L2. b) Write an equation for the plane containing L1 and L2. 3. (10 points) a) Find the coordinates of the point of intersection of the line at = 2+ 3t, y = 1 +t, z = 4+ 2t and the plane 21: + 53/ + 2z = 2. b) Find the distance from the point (2, 1, 4) to the plane 22: + 5y + 22 = 2. 4. (10 points) Find the area of the triangle with vertices P, Q, and R, if P has coordinates (2, —3,0), Q has coordinates (5,1,2), the vector FR is parallel to i +j + k, and the vector (W is parallel to 4i + 8j. 5. (10 points) Find the volume of the box determined by the vectors u = 2i — j — k, v = j + 5k, and W = i + 3j. 6. (10 points) The velocity vector of a particle at time t is v(t) = egti 7 (sint —« 1)j — gt3k. a) Find the position vector of the particle r(t) if r(0) 2 i + j. b) Find the acceleration‘vector a(t). . . . . . . - . . x — y — 2 7. 10 pomts Find the hunt 1f 1t eXISts: 11m —————————. ( ) (z,y)n~(4,2) f — x/y + 2 8. (10 points) Find the limit if it exists: lim y sin(—1-). Chico—«010) :1: . . l 9. (10 pomts) Describe the domain and range of the function f :1:,y = ————— . Which < ) ~——y _ m, _ 2 of the following properties does the domain satisfy: open, closed, neither; bounded, unbounded? 6x ’ 8312 ’ agar 10. (10 points) Find the partial derivatives if f (51:, y) = $6295” — cos(;ry). ...
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