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Unformatted text preview: MATH 223 SECTION 12  FALL 2009  EXAM 2 Monday, October 12th, 2009
Name You must show all of your work in a. clear form to receive credit. l. The temperature (in degrees Celsius) in a. lake is given by
T(a:, y, z) = my2 + .1136”. Fred the fish is at the point (1, 1, 0). (a) Will the temperature (instantaneously) increase or decrease if Red
heads in the direction toward the point (3, —1,0)? [10 points] ,_ i” 5 ‘9 . VT:(\\1+5X‘J \‘:+k2K1+2‘KJ\3 4' “[xev K =5 VTl‘J‘Cn =' + 2; +1.
\4 c: 21" w23 and..th “4,, 71% VTU.\;Q'¢= (5% =‘l70 =5 Jame ..;.\\ RAMSCJ 2 MATH 223 SECTION 12  FALL 2009  EXAM 2 (b) Red is feeling toasty. Which direction should he head to decrease
the temperature most rapidly? (Give your answer in the form of a
vector.) [10 points] “I. skaJA W “N. ”W\‘«‘\A='l\?r2j "‘2 (c) If Fred heads in a direction that is 30 degrees from your answer to
part (b), what would be the rate of change of temperature? [10 points] “WUMON“? $27 '— ‘ .. i.
V  \\VT\\ @553 = SSﬁ c.5550. MATH 223 SECTION 12  FALL 2009  EXAM 2 3 2. Use the contour of f (32,31) below to determine the sign (4, , 0) of
the following: [3 points each] 3. Consider the surface z = f(x, y) = 32:2 + y3 — 63y + 3 (:1) Find and classify any local extreme (min/max) values. [12 points] 4 MATH 223 SECTION 12 — FALL 2009  EXAM 2 (b) Give an equation for the tangent plane at the point (1,1,1). [8
points] $K\‘B=O , thr—3 —3~(‘r\ 2—\= (c) Give a vector that is normal to the surface at the point where :L' = 2,
y = 1. (Note: your answer should be a. vector in 3space). [8 points] ('— Ld: P A' Mr M..A\ Q (nah  3 :sV—F= m‘h" £‘(7\\\Y +' 91(2\A (7L *qs"" 1 ‘Fl 3‘:— 3‘5 MATH 223 SECTION 12 — FALL 2009  EXAM 2 5 4. Let f(a:,y) = zyz + ycos($), where m = 58‘ — :32 and y = 23 + t2.
Find g at the point (s,t) = (1,0). [10 points] E a:
3K 2:5 7:35 3‘1
31 293 H +. 1. (1 6 MATH 223 SECTION 12  FALL 2009  EXAM 2 5. Electrical power is given by P(E, R) = 3%, where E is voltage (in
volts) and R is resistance (in ohms). If E = 200 volts and R = 40
ohms, use differentials to estimate the change in electrical power if the voltage is decreased by 20 volts and the resistance is increased by 5
ohms. [10 points] a? sf.
6?: 3E Ag + 3% AR 6. Determine the sign (+, —, 0) of the following integral (Hint: you
should not try to compute the integral) [10 points] fx2—di
D ...
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This note was uploaded on 09/23/2010 for the course MATH 216 taught by Professor Dickson during the Spring '10 term at UAA.
 Spring '10
 DICKSON
 Math

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