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1.[-12Points] l DETAILS I LARCALC1213.1.020. Evaluate the function at the given values of the independent variables. Simplify the results. fix, y) = 3x2 4y (a) Wmec. AX S .V S 11. [I3 Points] DETAILS LARCALC12 13.8.028. Use a computer algebra system to graph the surface and locate any relative extrema and saddle points. (If an answer does not exist, enter DNE.) z = exy relative minimum (X, y, 2) = ( ) relative maximum (X, y, 2) = ( ) saddle point (X, y, Z) = ( ) 12. [-/1 Points] DETAILS LARCALC12 13.10.027. Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated point. Surface Point Plane: x + y + z = 1 (9, 1, 1)13. [-/2 Points] DETAILS LARCALC12 13.10.029. Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces. Cone: x + yz - z2 = 0, Plane: x + 2z = 4 f( =14. [-14 Points] DETAILS LARCALC12 13.3.084. Find the four second partial derivatives. Observe that the second mixed partials are equal. 2 = 14xey 13ye_x mm 15. [-/3 Points] DETAILS LARCALC12 13.8.501.XP. Examine the function for relative extrema. (If an answer does not exist, enter DNE.) f(x, y) = 9x2+ 6y2- 18x- 12y+ 13 relative minimum (x, y, z) = relative maximum (x, y, z) = saddle point ( x, y, Z ) =2. [-/1 Points] DETAILS LARCALC12 13.2.052. M Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x, y) - (0, 0) implies r -> 0.] xo+ 8 lim (x, y) - (0, 0) x +3. [-/4 Points] DETAILS LARCALC12 13.3.045. Find f and f, and evaluate each at the given point. f ( x, y) = exy, (In 5, 2) f ( x, y ) = f ( x, y ) = f (In 5, 2) = f (In 5, 2) =4. [-/6 Points] DETAILS LARCALC12 13.3.064. Find f , f, and f, and evaluate each at the given point. f ( x, y, z) = xy' + 2xyz - 6yz, (-3, 1, 3) fx ( x, y, z) = f ( x, y, Z) = f ( x, y, Z) = f (-3, 1, 3) = f ( -3, 1, 3) = f-( -3, 1, 3) =5. [-/4 Points] DETAILS LARCALC12 13.3.079. Find the four second partial derivatives. Observe that the second mixed partials are equal. Z = X - 3xy + 5y3 azz = 2x 2 azz = axay azz = ay 2 a2 z = ayax7. [-/2 Points] DETAILS LARCALC11 13.6.047F. Consider the function. f ( x, y) = 9 - X y 3 2 Find a unit vector u orthogonal to Vf(6, 9). U = Calculate D f(6, 9). DJ f(6, 9) =9. [-/1 Points] DETAILS LARCALC12 13.7.031. MY NOTES ASK YOUR TEACHER PRACTICE Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) x2 + 22 = 100, y2+ z2 = 100, (6, 6, 8)