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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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