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Unformatted text preview: MATH 251, Sumrner 2007 I E 0L) RAICH EXAM 1  VERSION B4 ' ‘
Name (printed): ’ I " Section #2 “On my honor, as an Aggie, I have neither given nor received unauthorized ,a'id,f.on this academic
work.” 1 Signature: UIN: it DIRECTIONS: 1. The use of a calculator, laptop or computer is prohibited. 2. Please present your solutions in the space provided. Show all your work neatly and concisely
and clearly indicate your ﬁnal answer. You will be graded not merely on the ﬁnal answer, but
also on the quality and correctness of the work leading up to it. ‘ ‘ ‘ 3. There are questions onBOTH SIDES of the paper. Please be aware of this. DO NOT WRITE BELOW! 1Disputes about grades on this quiz must be handled the day the quiz is handed back and must be discussed before
you leave the room. If the quiz leaves the room, it will not be re—evaluated (except for possible adding mistakes). 1 1. (10 pts) For what values of c is the angle between the vectors (1, 2, 1) and (1, 0, 2c) equal to 7r/3. A F" l M gamma ,_ , _.
<\xZ~D”<\\aZa=J_Z WM U23 +5 lac = l; dxw' Lt.) (; 2. (10 pts) Find the area of the triangle with vertices P(1, 2, 3), Q(1, 3, 2), R(—2, 1, —1). (l\3\7—/\
«mm W, A= lil<0~l¢l>><<r3x~lce> l 1
J“ +3 3. (10 pts) Determine the level surfaces of f (:13, y, z) = 33:2 — y2 — 222. \53’5‘V7‘W7sz‘ lbo “WWW oﬁ z sheds} W i ' 4. (10 pts) Find the equation of the tangent plane to :32 —~ 2y2 — 325+ myz : 4 at the point
(3, ~2, —1). FWth Xl—“Af «321+X‘y2 —‘l
\7F ‘ <1>< W2. ‘—W+Xé, ~éz HUD +3
Wham  (9+2. ‘8~3, we? t «a so) +3
ul pg
WWBX Ls'l \Im: O lﬁwé‘v = El 5. (20 pts) Use differentials to approximate f (m,y) : 1n(3:1:  2y) at (m,y) : (41,494). “warm it frH 153 + Mam (Lu «(3 + Q H Skew *5) :I6+.Ob—_.1\ ,u: 3L
\00 6. (20 pts) The temperature atda point (as,y,z) is given by T(:1:,y,z) : lie—“E24312”3 where T
is measured in °C and 33,11], 2 in meters. Find the rate of change of temperature at the point
P(2, 1, —2) in the direction of the point Q(3, —2, 2). ._A .u I 2_ 23 v" (Z‘hl—l)
\7Ttxtyxzﬁ—He Y <2xﬂw321> 4.51 '
\7T(2\\t~2\: ~ ‘ “2"? (HAmzp, mi 
ad“ a <\\.‘3rL't> \
{41“ m t ““x : h“ <\\‘:5IL{7 WGJ W EL 7. (20 pts) Find 3 positive numbers whose sum is 115 such that m2yz is a maximum.
XWR: \5 Z: l3—x~\/ .
“VA/:21; XIV} I V
“Wm: X1V(\§~X~y)= \5x1y — xsy—Xlkf“ +471
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M (1U9~><~y\~»<\ to {Q WW *WO
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NW“ “(as \/= HlSVO
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if L51? X’Li‘ V‘ 2U?”
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I; E 1V X" 7” 4M1?) =‘=f(‘—c?>—QLE\L% = 4% W5 t5t4$~ztiz 05% 235
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This note was uploaded on 07/22/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.
 Spring '08
 Skrypka

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