sp02prelim2 - = (cos2t)i + (sin2t)j + tk. Find v(t), Iv(t)1...

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Math 192 Prelim 2 March 26, 2002 This is a closed book test. No calculators allowed. Show all work! i+(~)k 7r I) Let a(t) = (1- ~)i + (COS7rt)j + (sin7rt)k where t > 0. You are given v(I and r( I) = 4i + 2j + k. a) (8 points) Find r(t). b) (7 points) When is the speed the slowest? 2) Let P = (1,2,3), Q = (2,0,4) and R = (0,1,1). a) (8 points) Find a normal vector to the plane of triangle PQR. b) (7 points) Find the area of triangle PQR. c) (7 points) Find the equation of the plane containing triangle PQR. 3) a) (8 points) Set up and evaluate an integral for the length of that part of the curve given by x = 2t, y = 4 cos 7rt, z = -4 sin trt between t = 0 and t = 10. b) (8 points) Let r(t)
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Unformatted text preview: = (cos2t)i + (sin2t)j + tk. Find v(t), Iv(t)1 and T(t). 4) Let p = (0,2,3) and consider the plane 7[ given by x + y -2z = 4. a) (8 points) Find the equation of a line through p perpendicular to 7[ . b) (7 points) Find the point Q of intersection of this line with 7[ . c) (7 points) Find the distance from p to 7[ , that is the distance from p to Q Find the domain and range of f. Is the domain 5) a) (8 points) Let J(x, y) = In(l + xy) open, closed, bounded? b) (7 points) Does lim :: exist? (x,y)-+(O,O) y 6) (10 points) Say u and v are vectors such that lul > O and I vi > O u x v = v x u. What can you say about the angle between u and v? Suppose also that...
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This note was uploaded on 02/12/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).

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