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C3T2V2Solutions08

C3T2V2Solutions08 - MA 2-42 Test 2 Version 2 NO WORK=N0...

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Unformatted text preview: MA 2-42 Test 2- Version 2 NO WORK=N0 CREDIT!!! l. (10 points) Use f(x,y) = 11x2 + 34:2 to answer the following: a) State the damain and range of f.(x,y). Label your answers r) e: K? bOWnt R2 9'7 (Ciflll Xe E130) Rat/19542 L g; 26 or E30 1)) Draw and clearly label level curves of f(x.y} = fix: + y?‘ for k = 0, l, 2 in the xy plane. OCXiXa+Y2 %K:0)L¢:C7 i : 3,32%}; l: ){2'4' 72 2. (15 points) Find and classify the critical points of f(x,y) = 3).}! — x3 - 3:3 5 91:3ljf3LZ 57C; L)‘:_>L‘“ r2 . 3‘17: 3X “572 3 741%; ‘5’ Si: (:42) :séq‘ Xia'?’ :0 XL»: 0 “Was-l XCxfia-DZO Cl’l-H‘C (I ol‘n’r‘gr (3)0) Goad (M1) X50 X: Dom : 3M 70 __ Rxfi,l}l\: “—éé O 3. (15 points) Givenfo,y) = xay“ « xlny :1) Find the equation of the tangent plane to the surlacefoi y) at the point (3 1). Clearly label 211 ofyourw.0rk Z ($(Q b3: —-—Q<(CL;\D§ (XLL3 f 3C7{0kgb>(&7“ b I1><32><i71lwlfl7* @745)”: Q J}? W2 3—5- 1976313 33, 5: 33 ‘l 313 a 4 : 4&6) + 53(3’23 b) Find the linear approximation offlx y] at (3 1) and use it to approximateflill .3). After plugging into the formula you need not simplify. Lump 5743;0033 +3367 l3 H3r2,1,33 2? 33(342—433 +35 (n3!) 4. (12 points) Use f(x,y) = l,n(7y + 3):); + 2) to answer the following: 21) Find the direction of the maxi mum rate of change- of f at (1,0) T79: 43 £313,231. 213113.33» b) Find the value of the maximum rate ofchange of f at (I 0) 1VH1JO3“ lW: @CE 5. (20 points.) Use w =632_'FI; x = 43 H. y = J; in the following: Be sure to clearly label all the derivatives you take- 21) Write out the farmula for fl and then use it to find fl :5 83 83 ML) A if“ :: Lu a3 —— ix % £13 9,1” c) * * * Extra Credit (2 points): State the regult of Clairaut’s Theorem “‘ * * QKLT '5 £7 X. 6. (10 points) Show and explain why the following limit does not exist ‘ A mac/‘54 vile )H‘AJUfi . 33g}! i3? . lim iim O 3 13W 2 “O u.y‘1—i{0.fl} x1 + 3.- Afigp‘OGufl-a \xL‘C’k [RM 3K MG; __ it?!“ 2 L/.: >42 CXJXQ—BmxojU) X2+ XZ' .. x90 a 3 1542' E: 04:52“ (I‘M‘f‘i’ A093 {10%— 62433“? 7. (18 points) Find the-absolute maximum and minimum values of f on the set D, where f(x,y) = x2 + ya —2y and D is the closed triangular region with vertices (0.0), (0,1), («10). Make sure- y-Ou graph D on-the xy - plane and clearly label all of your work. ...
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