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Test2Solutions

# Test2Solutions - Name Section Math 234 Sections l—3 Test...

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Unformatted text preview: Name: Section: Math 234: Sections l—3 Test 2 March 2.; 2010 The exam is all partial credit. Please write {leatly and clearly, showing all of your work. No calculators, cell phones, books, or notes- may be used. The test contains \$00 possible points. Good luck? Question Points 1. (10 point-s) Suppose a. particle moves in the any-plane with veEocity and initial pusition given by vm : ME”), rm) : <‘—3,5>. Find the poaition fumction r(t). New ‘ “my”? :57- 1.. 5194‘? I”; W ”5”?“ { mm “w ”(:33 m” w ,. . ~ "1 M “M g % {I V ‘w-w ,4? WW M I ,JF a.“ A“ ‘ W 5:“; a“ “r «r 3 ex: Mil; {y Ma”? g 5 ff" 1 ts M «3% «mm» x! g <an I m M , 69 “m” x u m i s: w W’- “i w ”m N s a? “a v 0:; 2. Suppose a particle maves in three—dimensional Space with position given by 1 4 . m 3 5:2, 533/221», 2 g t g 4. (a) (5 paints) Find the velocity and acceleration at time t. (b) (7 points) Find the total distance. traveied by the i)&rti(:ie between times t m 2 and t 2 4. 5% 'r‘; a; . M. Wmnmmn‘w; MW“ ' MWMW . :i: J A . 2: if 1““? g «a? ﬁg; 2 g m " , in n 9' _ i , in?" g: ENE, “1% 6]} ix A: g; has-w- E; a m} A I w. w ’ =1. ’1‘ W, "“"Tx x i i? l W. Find the domain of. f and draw level curves for f m .25, 1, 4. 3. (10 points) Let f(3:,y) : 4‘ (15 points) Calculate the following limits 2 _ 2 (a) lim W (msy>‘~-v(~3,3} a: + y A. . WM w“: magi; ‘7. ‘3 W ‘ - :17 .- m y" €i1&§%ci?‘*”.lm- ﬁa‘i‘ﬁ (‘0) 11111 W (a » \$5194?ng (m,y)—>(0,[}) a: +1} ' NM f“: ' ”12:,le :3; £3 (‘4'! . Every month: a baker produces 20 thousand loaves of white bread and 30 thousand loaves of wheat bread. The. bakery’s monthly proﬁt is 23 thousand dollars It estimates that increasing monthly pro“ duction of white loaves by 1 thousand will increase monthly proﬁt by 1 thousand dollars; it estimates increasing monthly production of wheat loaves by 1 thousand decreases monthly proﬁt by 500 dollars. (a) (7 points) Using linear approximation, estimate the monthly proﬁt if the bakery increases produc- tion to 22 thousand white loaves and. 32 thousand Wheat loaves per month. “33x 3:4 k} K. a3 {a "Mama-MM... MW , .th’W-lﬁw‘mmna.m M. ” ”w” --=--- (b) {3 points) How should the bakery change their production levels to most efﬁciently increase 1,3176%” (ie. should the increase or decrease White/ wheat production and in What ratio)? 6. (10 points) Suppose that ﬂu, v) is a differentiable function on R2 with u :2 :r, + y and v : :1: — y. Show that . 5f 3f 3f WM. ‘ “x. A? J 1% E i E L, mm v.25 7. Let z z. (1,?” = 5317183:+ cosw. (a) (8 points) Find the equation of the tangent piene to f at the point (\$0,210) 2 (0,1). 1’3 M '3' {b} (5 points) Find the deiinLtiVG of f at the paint (0.1) 111 the direction of the vect01{l~3 4). :EQ‘ £293 éwﬂgﬂ #1??? W; 7126134 “Ivar-«“1323 ng’ié?’ '52:: “”2 ¢ w<§g QE< < E KW ”3/3327: (‘th Mfr .ngWtW W. #2 W M W _ WW WWW W W ”“3“ """ gmam m We? w“ WWW WWAu- w (C) (5 points) If 2:05) : —3t, y(t) m (34:, find g]; at 2‘. : 0. 15%;” {WEE W :4 2 DO 4.. (15 mares.) Let fmm} : :r, + my + y2 w 631.4 (3,) Find and classify aii critic-M points; of f. (b) Find the absoiute maximum and minimum values of f on the cloged triangle with vertices (0:0), (4,0), and {4.4}. #15” any,» m m» ‘ M £14; g» “V Wwwwmm-wmumﬁmacaw. ”n ' 2- ‘ i: 3’ ‘ “ W4 ‘7 a: g WW5» “W" ‘, g5 _ m if.» E . ' ““‘«u._‘_ru4:<7.nw,ww.m.‘“mm-“Mna. :E i ' 3%; a»; A “a: W w . 2' e__ i.) AWN ~§ 4 ...
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