1. For xyxyxf 32),( +=, find )3,2(f A. 8 B. 18 C. 26 D. 22 E. 10 2. Given yxxyyeyxf2332),(++=, find yf∂∂ A. 23xye + B. xyxyye 626 ++ C.xyy 632 + D.2326 xxyye ++ E. 326 ++ yye 3. Given )2sin(),( yxyxf =, find )3,1(πxf A. 23 B. 6π C. 1 D. 2π E. 3π4. Given yxyxf2),( =, use linearization and the values of yfxff ,, at )2,4( to estimate )97.1,02.4(f A. 96.7 B. 08.8 C. 12.8 D. 20.8 E. 24.8 5. Given xyeyxf3),(=,find yxf∂∂∂2 A. xyey329 B. xyxye39 C. xyex329 D. xyexy3)39( + E. xyexy3)69(+6. Given xyyxxf633)(−+=, please choose the correct statement about its relative Max/Min or saddle point. A. There are 1 relative max and 1 relative min. B. There are 1 relative max and 1 saddle point. C. There are 1 relative min and 1 saddle point D. There is only 1 saddle point, no max/min. E. There are 2 saddle points.7. A flat metal plate is located on a coordinate plane. The temperature of the plate, in degrees Fahrenheit, at point ),( yx is given by yxyxyxT64232),(+−+=. What is the minimal temperature? A. F°−3 B. F°−4 C. F°− 7 D. F°−10 E. F°−11 8. Evaluate dydxyxx)2(020+∫∫ A. 38 B. 314 C. 316 D. 10 E. 49. Let yxyxf+=),(, G is the plane region between the graphs of 2xy = and xy=, find dydxyxG)(+∫∫ A. dydxyxx)(010+∫∫ B. dydxyxxx)(102+∫∫ C. dydxyxxx)(102+∫∫ D. dydxyxx)(110+∫∫ E. dydxyxx)(1102+∫∫ 10. )(xg is the unique solution to the initial-value problem: ==2)1(ln)('gxxg Evaluate the value of )2(g A. 22)2(ln21)2(+=g B. 22ln2)2(+=g C. 32ln2)2(+=g D. 12ln2)2(+=g E. 22)2(ln)2(+=g11. Let )(xf be the unique solution to the second-order initial-value problem: ===.1)4(',4)4(,2cos)("πππffxxf Evaluate the value of )0(f A. 41)0(π+−=f B. 8)0(π=f C. 24)0(π+−=f D. 841)0(π+−=f E. π8341)0(+=f 12. What is the slope of the direction field of yxy+=' at point )2,1(− ? A. 2− B. 1− C. 2/1− D. 1 E.