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____ 6. Use Lagrange multipliers to find the maximum value of f(x,y)=x2 +3xy+y2 where subject to the constraint x2+y2?9 a. b. c. d. e.   ____ 7. Use Lagrange multipliers to minimize the function f(x,y,z)=x2 +y2 +z2 subject to the following two constraints. X +8z=6 X +y=12 Assume that x, y, and z are nonnegative. a.108 b.72 c.324 d.216 e.36   ____ 8. Use Lagrange.
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14.5 Surface Area Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the area of the portion of the surface z = 8x + 4y that lies above the triangular region with vertices (0, 0), (2, 0) and (0, 2). a. 4 b. 36 c. 18 d. 162 e. 324 ____.
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  ___ 16. Determine the continuity of the composite function f ?g where and g(x,y)=5x-8y. a. continuous except at b. continuous for all c. continuous for all d. continuous except at e. continuous everywhere   ____ 17. Find the limit for the function f(x,y)=4x2-5y. a.-5y b.0 c.4x d.5y e.8x   ____ 18. Find the limit for the function f(x,y)=8x2-6y . a.8x b.-6 c.0 d.16x e.6y   ____ 19. Find the limit .
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13.4 Differentials   Multiple Choice   Identify the choice that best completes the statement or answers the question.   ___ 1. Find the total differential of the function Z=2x8 y3. a.dz=16x8 y3 dx+6x8 y3 dy b. dz=48x7 y3 dx+48x8 y2 dy c. dz=2x2 y8 dx+2x3 y7 dy d. dz=16x7 y3 dx+6x8 y2 dy e. dz=6x2 y8 dx+16x3.
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  ____ 6. Find an equation of the tangent plane to the surfaceg(x,y)=x2-y2 at the point(2,3,-5) a.4(x-2)-6(y-3)+(z+5)=0 b. 4(x-2)-6(y-3)-(z+5)=0 c. 2(x-2)-3(y-3)-(z+5)=0 d. 4(x-2)+3(y-3)-(z+5)=0 e. 4(x-2)+6(y-3)+(z+5)=0     ____ 7. Find an equation of the tangent plane to the surface at the point (5,-1,1) a. b. c. d. e. . ____ 8. Find an equation of the tangent plane to the surface.
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  ____ 11. Describe the level curves of the function. Sketch the level curves for the given c-values. z=6-2x-3y, c=0,2,4,6 a.   b.   c.   d.   e. ____ 12. Sketch the level curves of the function for the given c-values c=0.2,4,6 a.   b.   c.   d.   e.   ____ 13. Sketch the level curves for the function for the given.
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  ____ 6. Examine the functionf(x,y)=5x2-6y2-30-36y+9 for relative extrema and saddle points. a. b. c. d. e.   ____ 7. Examine the function for relative extrema and saddle points. a. b. c. d. e.   ____ 8. Examine the function f(x,y)=x3-18xy+y3+7 for relative extrema and saddle points. a.saddle point:(0,0,7):relative minimum:(6,6,-209) b. saddle point:(6,6,-209):relative minimum:(0,0,7) c. relative minimum:(0,07);relative maximum: (6,6,-209) d. relative minimum:(6,6,-209);relative.
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  13.10 Lagrange Multipliers   Multiple Choice   Identify the choice that best completes the statement or answers the question.   ____ 1. Use Lagrange multipliers to minimize the function f(x,y)=x2-y2 subject to the following constraint:  x-6y+45=0 Assume that x and y are positive. a. b.0 c. d. e. no absolute minimum     ____ 2. Use Lagrange multipliers to.
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  ____ 11. List the critical points of the functionfor which the Second Partial Test fails. a. b. c. d. e.   ____ 12. Find the critical points of the function f(x,y,z)=(x+7)2+(7-y)2+(z+6)2and from the form of the function, determine whether a relativemaximum or a relative minimum occurs at each point. a.relative minimum at (7,-7,6) b. relative.
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14.6 Triple Integrals and Applications Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Evaluate the following iterated integral. a. 428 b. 438 c. 431 d. 442 e. 432 ____ 2. Evaluate the following iterated integral. a. b. c. d. e. None of the above ____ 3. Evaluate the iterated integral . a. b. c..
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____ 6. Find using the appropriate Chain Rule forw=y3-8x2‑y wherex=e3 and y=et, and evaluate the partial derivative at s=-3 and t=2 Round your answer to two decimal places. a.1,209.99 b. 806.71 c. 1,210.14 d. 806.69 e. 1,209.20 ____ 7. Find using the appropriate Chain Rule w=x2+y2+z2 for where x=8t coss, and z=8st2 a.64st4 b.128s4 c.16s4 t d. 128st4 e. 16st4 ____.
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  ____ 6. Given f(x,y)=16-x2-y2, use the total differential to approximate at (2,3) towards (2,22,.1.04) Round your answer to two decimal places. a.10.96 b.-6.04 c.49.96 d.31.92 e.33.92   ____ 7. Given , f(x, y)=x cos y,  calculate by evaluating f?(4,6)and f(2,3,1.05). Round your answer to four decimal places. a.7.3037 b. 5.6074 c. –16.6963 d. –2.6963 e. –21.3926   ____ 8. Given f(x,y)=x cos y, use.
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13.2 Limits and Continuity   Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find by using the limits and a.7 b.2 c.3 d.-3 e.-4 ____ 2. Find by using the limits and a. b. c. d. e. ____ 3. Find the limit. lim (x+5y+5) (x,y)?(0,0) a.10 b.6 c.0 d.11 e.5   ____ 4. Determine the continuity.
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  13.8 Extrema of Functions of Two Variables   Multiple Choice Identify the choice that best completes the statement or answers the question.   ___ 1. Identify any extrema of the function g(x,y)=(x-2)2+(y-1)2 by recognizing its given form or its form after completing the square a. b. c. d. e.   ____ 2. Identify any extrema.
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Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Evaluate the following integral. a. b. c. d. e. ____ 2. Evaluate the following integral. a. b. c. d. e. ____ 3. Evaluate the following integral. a. b. c. d. e. ____ 4. Evaluate the following iterated integral. a. 41.5 b..
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  ___ 6. Determine the continuity of the function . a. continuous except at(4,0) b. continuous except at(4,2) c. continuous except at(0,0) d. continuous except at(0,2) e. continuous everywhere   ____ 7. Find the limit. a.5 b. c. d.0 e.   ____ 8. Determine the continuity of the function . a. continuous except at(0,11) b. continuous except at(2,0) c. continuous except all y?0 d..
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  ____ 11. Use Lagrange multipliers to find the minimum distance from the plane x+y+z=5 to the point (8,7,7) Round your answer to two decimal places. a.3.00 b.15.67 c.9.00 d.9.81 e.96.33   ____ 12. Find the highest point on the curve of intersection of the following surfaces.  Cone:x2+y2-z2 =0 Plane:x+16z=4 a. b.64 c. d. 68 e. 60   ____ 13. A cargo container (in the.
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  13.9 Applications of Extrema   Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5. a. b. c. d. e.   ____ 2. Find the minimum distance from the point (-5,-5,0)  to the surface a. b. c. d..
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____ 6. Convert the integral below from rectangular coordinates to both cylindrical and spherical coordinates, and evaluate the simpler iterated integral. a. b. c. d. e. ____ 7. Use cylindrical coordinates to find the volume of the solid inside both . a. b. c. d. e. ____ 8. Use cylindrical coordinates to.
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  Multiple Choice   Identify the choice that best completes the statement or answers the question. ____ 1. Find using the appropriate Chain Rule for w=x2 +y2  where x=7t and y=3t. a.116t b.58t c.104t d.32t e.174t   ____ 2. Let w=cos (4x-4y) where x=t9 and y=3 Find a. b. c. d. e.   ____ 3. Let w=xy cosz, where ,x=t3 y=t5,.
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14.4 Center of Mass and Moments of Inertia Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the mass of the lamina described by the inequalities given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.) a. 768 b. 128 c..
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____ 11. For , evaluate f(x,y)= sin (7xy), at fx the point a. b. c. d. e. ___ 12. For (x,y)=sin (9xy), evaluate,fy at the point . a. b. c. d. e. ____ 13. Find the first partial derivative for the function f(x,y,z)=5x2 y-3xyz+6yz2 with respect to z. a. fz(x,y,z)=-3xz+9yz b. fz(x,y,z)=-6xz+12yz c. fz(x,y,z)=12xz+15yz d. fz(x,y,z)=3xz+12yz e..
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14.7 Triple Integrals in Other Coordinates Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Evaluate the following iterated integral. a. b. c. d. e. ____ 2. Evaluate the following iterated integral. a. b. c. d. e. ___ 3. Evaluate the iterated integral . a. b. c. d. e..
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the temperature in degrees Fahrenheit. The wind speed is miles per hour and the temperature   is Fahrenheit. Use to estimate the maximum possible propagated error in calculating the wind chill. Round your answer to four decimal places. a. Dc=±8.4405 b. Dc=±9.8810 c. Dc=±2.4405 d. Dc=±8.8810 e. Dc=±5.4405     ____ 12. Suppose the formula for wind chill C.
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  ____ 6. Find and simplify for the given function f(x,y)=7x+2y2 a. b. c. d.7x e.   ____ 7. Describe the domain of the function . a. b. c. d. e.     ____ 8. Describe the domain of the function f(x,y)=In(6-x-y). a. b. c. d. e.   ____ 9. Sketch the surface given by the function f(x,y)=6-2x-3y. a.   b.   c.   d..
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    13.7 Tangent Planes and Normal Lines   Multiple Choice   Identify the choice that best completes the statement or answers the question. ____ 1. For the function given by describe the level surface given by . a. sphere of radius 4 centered at the origin b. circle of radius 4 centered at the origin c. elliptic.
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  Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find and simplify the function f(x,y)=7-2x2-5y2 at the given value (3,3). a.-56 b.-26 c.-14 d.-44 e.-27 ____ 2. Find and simplify the function f(x,y)=4-6x2-3y2 at the given value (t,2). a.-6t2 b.-8-6t2 c. -4-6t2 d. -16-6t e. .8-6t ____ 3. Find and simplify the function h(x,y,z)= .
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