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Math211ExamII_f04 - MATH 211 EXAM II 1)Determine for the...

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Unformatted text preview: MATH 211- EXAM II -OCTOBER 20, 2004 1 )Determine for the planes x-y—z=1 and 2x+3y-Z=5 a)The equation of the line of intersection b)The angle between the two planes 2)Determine for the position vector R = (t2 + l)i + t3 j +(t — 2)k , a)The acceleration vector at t=1 b)The equation of the plane containing the acceleration and velocity vectors at t=1 3)Evaluate the limits if they exist (show all work) a) lim xy (mam) 4x2+4y2 b lim xy ) (xy)+(0.0) 4x2+4y2 c) lim (xy>»<o,0) x2” 4)For the function 2 = x + 1n y + xy2 cosx Evaluate at the point (%, 2) Oz a) E 622 b) 6xr3'5y a 2 C) 6x¢9y2 5)Determine the local extrema locations (critical points) for a)z=xy2+ %+y2+10 h) z = 2(x +1)2 +302 — 2)2 + 602—2) 6)Determine, using the chain rule, for w = xez + zy a)??? at t=1, where x=+, y=t3 and z=t-1 b) a_w at u=l and V=l, where x=u2+v , y:uv2 2 2 av ,z=v —u ...
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