math241 f04 exam1 - October 8 2004 Math 241 Exam 1 V You...

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Unformatted text preview: October 8, 2004 Math 241 Exam 1 V. You must show all work. No credit will be given $31127 correct answers if work is missing or incorrect. N31 ' ' V» 77 D ’1'}; Let :62 —- y2 — 422 = 4. (a) Describe the traces of the surfaces in the planes cc = k, y = k, and z = k. (b) Sketch the graph. 2. Let 7' = 2 sin6 represent a surface in cylindrical coordinates. (a) Sketch the graph. 1 (b) Write the equation in Cartesian coordinates. (0) Write the equation in spherical coordinates. V 3. Let 2 2 3 4 2 a: + my + y —————- f , 0,0 , 0 if (23,11) = (0, 0) / I Find the largest set on which f is continuous. You must justify your answer. 4. Let 2 = elm2+3y+4z). 82 Use implicit differentiation to solve for — 6n 5. Letf($, y,z z)=:c4 +y3 +22. flste a linear approximation to f (a: y,z z) to approximate (1. 02)4+ +(1.97)3 + (3.01)? V, ——————— “6713a w~== y“. —— 3 (a) Evaluate 8—211. 8x / 311) (b) Evaluate — 6y 7 Let Z- — f($ y) Where :8 — 9(8 75,11) ( ,t),9(1 0) = 2, 41,0) = —2, gt(1, 0)-— — 6, h(1, O) = 3 h (1, O) = 5, h=t(1,0) = 4, 1(2,3) = —1, and fy(2, 3) = 10. Evaluate 821/83 and 02/61? when 5— — 1a ndt = O. 2 «L7 xx“ [/2 \‘ 1/ g ax «Cor LOOrkgfi Mag 22. _ K . é V F2 {-1 .. ,- W . :5 x 53 be M 3 W.“ WWWWMWWW} “i ‘1 ...
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