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6. Find the local linearization of g(u, v)==' +2uvat (1,2). Use it to estimate the change...
6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy. 6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy.
please show all work 245 1) Sketch the region represented by 55 dydis on the attached grid. DA 2) SET UP the integral for both orders of integration of R: region bounded by y = x, y = 2x, x = 2 SS Vx++y* dxdy 3) Evaluate the following integral by converting to polar. 4) Use a double integral in polar to find the volume of the solid bounded by the equations z = x + y +1,2-0, x +...
My professor said " Hint: Use change of variables formula u= xy, v= x^2 - y^2" 31. Consider the triple integral II w 2x dv, where W is the solid three-dimensional region bounded by the surfaces z = x2 + y2, z = 2(x2 + y2), and z = 1. Express it as an iterated integral in cylindrical coordinates. Do not evaluate it.
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integral dy dx into an integral over G, and evaluate both integrals a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then...
20. Show that the second derivative test is inconclusive when applied to f(r, y) 2 at (0,0). Describe the behavior of the function at the critical point For the next few exercises things to know are: 1. In a closed and bounded region, a continuous function will assume a maximum value and it will assume ImIIm valuic. 2. These values have to be assumed either at a critical interior point or on the boundary. They canot be assumed anywhere else....