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1. [-13 Points] DETAILS LARCALC12 11.1.007. Find the vectors u and v whose initial and terminal points are given. Initial Point Terminal Point "I (0, 0) (6. -2) VI (2. 7) (9. 5) Are u and v equivalent? Yes No 11. [-/3 Points] DETAILS LARCALC12 13.3.058. Find the first partial derivatives with respect to x, y, and z. f ( x, y, z) = 3x2y - 8xyz + 7yz2 f ( x, y, z ) = fu ( x, y, z) = f ( x, y, z ) =12. [-/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) f ( x, y, Z ) = f ( x, y, Z) = f ( x, y, Z) = fx( -3, 1, 3) = f ( -3, 1, 3) = fz(-3, 1, 3) =13. [-/4 Points] DETAILS LARCALC12 13.3.079. Find the four second partial derivatives. Observe that the second mixed partials are equal. Z = X' - 5xy + 2y3 azz = 2x2 azz = axay azz = ay2 azz ayax15. [-/4 Points] DETAILS LARCALC12 13.5.019. Consider the following. w = xyz, x = s + 5t, y = s - 5t, z = st- (a) Find aw/as and @w/at by using the appropriate Chain Rule. aw as aw = at (b) Find aw/as and aw/at by converting w to a function of s and t before differentiating. aw as aw at16. [-/3 Points] DETAILS LARCALC12 13.5.036.MI. Differentiate implicitly to find the first partial derivatives of w. x2 + 12 + 22 - gyw + 6w2 = 7 aw ax aw ay aw = az17. [-I3 Points] DETAILS LARCALC12 13.8.009. MY NOTES ASK YOUR TEACHER PRAC'I Find all relative extrema and saddle points of the function. Use the Second Partials Test where applicable. (If an answer does not exist, enter DNE.) f(x,y)=x2+y2+4X10y6 relative minimum (X, y, 2) = ( > relative maximum (x, y, z) = 19. [-/2 Points] DETAILS LARCALC12 13.10.005. Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize f(x, y) = x2 + 2 Constraint: x + 2y - 10 = 0 f( =2. [-11 Points] DETAILS LARCALC1211.1.055. l M' Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive X-axis. ||u||=2, 9u=9 ||v||=1, 9v=2 Hp: 20. [-11 Points] DETAILS LARCALC12 13.10.028. Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated point. Surface Point Cone: z = V X2 + y2 (6, 0, 0) S 3. [-I1 Points] DETAILS LARCALC12 11.2.066. Determine which of the vectors is (are) parallel to 2. Use a graphing utility to confirm your results. (Select all that apply.) 1 has initial point (5, 4, 1) and terminal point (2, 4, 4). n++n 7i 6j 2k 14i + 16j 6k 14i 16j + 6k i + 4j 2k i 4j + 2k None of these vectors are parallel to z. 4. [-12 Points] DETAILS LARCALC12 11.3.043. Consider the following. u=9i2j4k, v=4j+4k (a) Find the projection of u onto v. (b) Find the vector component of u orthogonal to v. S 6. [-11 Points] DETAILS LARCALC12 11.5.052.M|. Find an equation of the plane with the given characteristics. The plane passes through the point (2, 0, 1) and contains the line given by g = S