Use a graphing utlity with wertor copa bilities to fnd Ux V U= (-1,4,1), v=(4,1,4) Shaw that uxV is s or theg anal to both u and V. (uxv). u- コ (uxv).v-

Q: Evaluate the Jacobian of G(u, v) = (u3 + v, uv) at (u, v) = (2, 1).

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Q: Use Lagrange multipliers to find the distance from the point (3, 0, -1) to the plane 6x - 4y + 7z +…

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Q: Use Lagrange multipliers to find the point on the plane x-y+z=7 closest to the point (4,5,1).

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Q: Describe how to find the Jacobian of x and y with respect to u and v for x = g(u, v) and y = h(u,…

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Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: Find the average value of f(x, y) over the plane region R.

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Q: Suppese That z is guen in implicit form by the equation : X°y -yz?+ X = 16 enviroment %3D in an of…

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Q: Find length of the cardioid r-a03from 0 0 to 0 t %3D

A: To find Length of cardioid r=aθ3  where θ=0 to θ=π

Q: det TiP M,2 be defined by -Q,X + QX + agX ). Show that ī is a linear transforimation and find T…

A: The solution is given as

Q: If f(u,v,w)=u+v2sinw  and u=x−y, v=y−z, w=z−x find  fx+fy+fz=?

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Q: Find the EXACT Jacobian a(x,y) d(u, v) 1 1 - -— (9u - 4v), y = —— (3u +3v) 4 4 X = for the following…

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Let (x,y,z) be the point which is closest to the point (2,4,0) .

Q: 8. Use change of variables to find: a) The Jacobian if x=(u+3v), y =; -(v- 2u).

A: We will use concept of change of variables.

Q: Find the Jacobian of following functions f(x,y,z) = 3xy – yz + 2y³z² – 5xyz³ g(x,y, z) = xyz – x³yz…

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Q: Find the Jacobian for the indicated change of variables. x = uy -2u, y = uv О д(x,y) H(u, v) О…

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Q: 5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0),…

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Q: Hewin If Z =R Cxxy]:and u=x-yg V=x²-y 그를 + show that

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Q: 24yıy2, 0< yı < 1, 0 < y2 < (0, fV1, y2) = %3D elsewhere Find the cov(Y,,Y2) is it possible for Y,…

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Q: Give an example of (v1, v2, v3) and (w1, w2, w3) independent se- quences in the R“ such that…

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Q: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

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Q: , find the Jacobian ?(x, y)?(u, v) for the indicated change of variables x = uv − 2u, y = uv

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Q: Evaluate ſ √x² + y²dxdy over the triangle with corners (0,0), (4,4), and (4,0) using x = u, y = uv.

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Q: Find the Jacobian ",Y,2) where u = yz, v = z, w = x + g 8(u,v,w)

A: We have been given  u=yz,v=z,w=x+y First, we will convert the functions x, y, and z in terms of u,…

Q: Let Ebe the hemisphere described by Oszs V1-x² -y? | and F=Vz2 + x² + y? i+• v²j+Vz? + x² + Compute…

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Q: Use Green's theorem to calculate where C is the rectangle with vertices (0, 0), (2, 0), (2, 3), (0,…

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Q: Find the standard matrx den ha statid competiten R2. Aenaflection about the line y= Collewed by…

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Q: Give an example of (v1, v2, v3) and (w1,w2, w3) independent se- quences in the Rº such that…

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Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y + z+ w= 6 3x…

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Q: In the xy plane mark all nine of these linear combinations: c[2/1]+d[0/1] with c=0, 1 , 2 and d=0, 1…

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Q: carulate the aistance between pointS k=(0,9) and . G7= -6,6) inthe.coordmate Diane. mo0 Cnuer :…

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Q: Evaluate p xy da + a dy, where C is the rectangle with vertices (0,0), (3,0), (3,6), and (0,6).

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Q: Let z = 3x*y, find Vz.

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Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

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Q: Use the Chain Rule to find ôz/əs and əz/ðt. z = tan(u/v), u = 4s + 7t, v = 7s – 4t Əz as az II

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Q: Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point…

A: First note that ,          if (x,y,z) be any point on tha plane x-2y + 3z = 6 then distance between…

Q: Sax Show that S,y = E(, -2)Y, Show that Cov(Y,F) = for all i. Use part a and b and linearity of…

A: According to our guidelines we are solving only first three sub-parts of a question and the rest…

Q: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

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Q: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

Q: Let d: R2 x R2 R be defined as follows. d((x1, y1). (x2, y2)) = 3/(x1 - x2)² + (y1 - Y2)². %3D Then…

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Q: Use Lagrange multipliers to find all points on the cone z2 = x² + y² that are closest to the point…

A: The solution has been given below.

Q: Prove: ZX is a perpendicular bisector of WY AZ MZ XZA7 = XZM7 :u

A: To prove: Side ZX is a perpendicular bisector of WY. Given: Triangle WZX and YZX is congruent…

Q: Evaluate 6. F.dī by Stoke's Theorem where F = y?i+x³j– (x + z)k and c is the boundary of the…

A: We have to use stoke's theorem .

Q: Evaluate //R V2x(y – 2x)dA where R parallelogram on the xy-plane with vertices (0, 0), (0, 1), (2,…

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Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: Determine the convexity/concavity propwity of the following: (iii) U(x, y) = xªyB,where 0 < a < 1…

A: Here first make the hessian matrix and then find Z^(T)HZ and check whether it is negative or not…

Q: Show that the dyfferential equatian IS exact x(スt5in t) do + cast -2tu) abe +x² dt-

A: We will show that the given differential equation is exact.

Q: let f(x, y, z) = 2x?y + 3xyz-x z+3y Find: fx . fxy, frz fryz

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Q: aw Find ди dw. and if w = x³ + In (-) + y, x = u? dv -+ 5 and %3D wwww y = 3v + 5u and point…

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Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

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