2008_06_03_11_53_42

2008_06_03_11_53_42 - Name: Discussion Section - No: DOS...

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Unformatted text preview: Name: Discussion Section - No: DOS Time: 14-5 Pofi'fln’flfl 11-5. in -__ '3: Midterm 2, Math 200 - Lecture D (Fali 2007) Duration: 50 minutes Please close your books, tum 01f your phrmcs and put, them mmy. You can use one page of handwritten. 'rerrrs. To yef. full credit you shoqu rzrrqiim'n your (answers. 0011’: fmyci to mite your name, ID number- and your TA ’5 Hanan. é: (3 points) Find all second order partial derivatives of the i'luu-tiuu f(:r.. y OiOCLba H a M- ): \/:r + 3F. Nud):‘1x+\f1 “f” (H ' 1 IV '55. -‘ EL "LL-(‘44ij :(E‘U grer : 1r» (7m!) 7 hi - 3 : ___"I;— 3 2 9x = 2;»; (13> ‘ n+7 a g“ (0") 2(0)“ 2(0) 1 CH : 2:)»; (2X7 2 23;] f) 9% (OH) : 2M“ O r: \m[02+\1“}+o'1 01L. lfiflwo'l H 1:” O.LH02H! 5’2 + 232 ( WW J ’51 2. Suppose you are climbing; a hill whose shape is given by the equation 1: = 1000 u 0.01:1;2 - 0.0213, where :r, y and z: are measured in meters, and you are standing at. a point with t-ot'irdinatus (100, 109, 700). The positive ar-axis points east and the positive y-axis points north. 1 f Zr (it, a. (3 points) In which direction is the slope largest. ? What is the mu)! 0 asg'gmt in that direction ? L. (N) "(l ..,M) 3 : lCCD » o . OI x3 — O. 02,): 2 f. . . / , : [00 f 517 / ;.-—-——-—""")‘2( ¥ /‘.r - -— Z 12 .— \COO « ovoipwm ' 0-0"! _/ , l—O - 04.1%; L ’ r- 0.02 (£0031 F200 3.3. (3 points) Find the extreme values of f(:::_./::_] = 32-51332 subject 1.0 t1 . constraint 3:"1 + y? + z") = 1. /|\(¥FY1?) T x) Y) _ZZ / . : ? "3‘: ~=> gm..er X”? +7 ‘ / fl?" x (2 points) Find the local maximum and Illinillnlm values and saddle points of the function 9(37‘ y) z 3:" + y" — 413:1}. 4. (5 points) Find the absolute maximum and minimum of f(:r. y) = 1:2 + y? + $23; + 4 on thoset R={(1'.y):—lss:sl,—1gyél}. mun :x’“+1’ W? +% " _ I .«--""‘ . K ( 3“) _f_\ F tpg/r‘FV /' /_‘ -§\X __ + 70 $ 2X: lX‘f or 1 r .J _ a x" L __ __ )_ __ Lt) _[‘ : 1 + X — C a X - 2V v ‘K ’15 2 L (X51): 13(474 DJ‘ITD -‘ 2x1 fl” 2 1‘ 2H} “7’ 2H3 + X- ‘l4l‘f / f2 l -_ \ W‘l —} -2."f2.(j ELK. _‘_) I'l- ‘i: F1 FF} —24 2(4) :1'FLH' x: A A —2 ‘1‘!"31” "1/. _ 21417 2 Lipid—D 1+1'x; L14 (4:0 274% ,/ 14XL _. \’;1‘ ----1 iii-{1) _' LL A 14 i 51%- ‘PI —=! 243(4)"!0 7W1 ...
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2008_06_03_11_53_42 - Name: Discussion Section - No: DOS...

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