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- y=- 1. T3,4) Set Up only Area bounded between the lines 2x+y=-2 (-1,0) 7x-y=17 X-y=-1 7x-y= 17 2 x +y= -2 and a) dx b)ag DELLWhich of the following is the normal line at the point (-1, 1, 1) to the surface x² − 2y² − 3²½ = −4 y Select one: ㅇ 부 x+2 y- 1 0 x+1 2 x+1 -2 블 2 부작괴 || = 4 -4 y+1 4 || = || = O None of them 부부뚝뚝 z-3 1 z-1 3 Z- -1 -3 z+1 3Consider the integral , 5y + 5x = 25, y - 4x = 0, and y - 4x = -25. (5y + 5a) dA where R is the parallelogram bounded by the lines 5y + 5z = 0 Compute the Jacobian corresponding to the change of variables u = 5y + 5x and v=y- 4x. The integral evaluates to > Next Question
- Find the equation of the line through P = (4, 12) such that the triangle bounded by this line and the axes in the firstquadrant has minimal areaAt what points does the normal line through the point (1, 2, 1) on the ellipsoid 4x² + y²+42² = 12 intersect the sphere x2 + y²+ 2² = 486? smaller x-value (x, y, z) = larger x-value (x, y, z) =39. Find all points on the portion of the plane x+y+ z =5 in the first octant at which f(x, y, z) = xyʻz² has a maximum 2 2 %3D value.
- Evaluate ∬S(x^2+y^2)dS, where S is the surface z=4−x, 0≤x≤2, 0≤y≤2.3. Consider a linear map T : R^ → R" with the property that null(T) = range(T). (a) For n = 2, provide an example of such a map. (b) For n = 3, prove that no such map exists.5. Consider the line that connects points (3,1) and (5,5). Find the surface area of the solid obtained by rotating the line around the x-axis.
- 22. Let D denote the region of the plane between the parabola y = 3 − x² and | the line y = x + 1. Computer- 2 dA.: List the vertices in R' of the convex region defined by Ax < b and x 0 where 2. A = 1 2. and b = 8. 1 1 6. (A) (0, 0. 0). (0,6, 0), (1, 1,0). (0. 2, 4), (1, 1,0), (3.2. 1). (3,0. 블), (0.3, 2) (B) (0, 0. 0), (0. 1,6), (0, 1, 1), (0. 2, 4). (1,0,0), (1,2, 3), (블, 0.3), (0, 3. 2). (C)(0.0.0). (6,0.0). (0., 1.0). (0. 2.4). (1,0,0). (1. 2. 3), (금, 1. 플), (0.3. 2) (D) (0, 0. 0). (0. 0.6). (0. 1.0). (0. 2. 1). (금,0. 0), (1. 2.3). (금.2. 플), (0.3. 2) (E) (0, 0. 0). (0, 6.0). (1. 1.0), (2.0.4). (3,0,0). (1.2. 3), (3.0. 플), (0. 3. 2) (F) (0.0. 0), (0. 0. 6). (0. 1. 0). (0, 1.4). (1.0,0), (2.2. 3). (중.0. ). (0.3.2) (G) (0.0. 0). (1.0. 6). (0. 1.0). (0. 2. 4). (금. 0.0), (1. 2. 1), (1. 0. 풍), (0.3.2) (H) (0, 0. 0), (0,0.6). (0. 1.0). (0, 2.4). (금. 0.0). (1, 2. 3). (금.0. 플). (0. 3. 2) 2: