{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

C3T2V2Solutions08

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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. ...
View Full Document

{[ snackBarMessage ]}