1) Given the mapping F(x,y,z)=(3e" ,xzsin 2y ,xy), v=(2,2,-1), using the definition, then the corollary (the Jacobian), compute the tangent map F, (v) at the point P-(-1,2,-2)

Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

Q: Find the linearizations L(x, y, z) of the functions in Exercise atthe given points.ƒ(x, y, z) =…

A: To findLinearizations of f(x,y,z)=tan-1xyz at (1,0,0) , (1,1,0) and (1,1,1)

Q: (B) Prove that the stream line of b are counterclockwise circles, for that calculate F = Vx (-y ěx+…

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Q: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

Q: b) Is there a linear map T: V → W, where dim V = 3, dim W = 4, rank T = 2, and dim ker T = 1?

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Q: 4. Let L: R² +R? be the linear map defined by L(x, y) = (x + y, I - y). Show that L is invertible.…

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Q: Evaluate F. dr where F(x, Y, z) = (1.25yz cos(xyz), 1.25xz cos(xyz), 1.25xy cos(xyz)) 1 1 and C is…

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Q: Evaluate | F· dr where F(x, y, z) (4yz cos(xyz), 4xz cos(xyz), 4xy cos(xyz)) and C is the line C 1…

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Q: Find the tangent plane for the level surface f(x,y,z) = 5x4 + cos (4y) + In (6z) = c at the point…

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Q: Given the map f:R-R+ defined by f(x.y.z) = (0,0,x.0) then nullity of f is: O A.4 O B. 3 OCO O D-2 OE…

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Q: 7. Find the Jacobian of the transformation T(x, y) = (w sin(v²),w cos(v²)). X=w Sin (v?) w = sin…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question (Q7) for you.…

Q: Let S (-7, 7) x Rx {0} and S2 = Image() where (u, v, 0) = (cosh v cos u, cosh v sin u, v). %3D…

A: Given: S1 = ( -π, π) * R *{0} S2 = Image (ϕ ) In which, ϕ (u,v,0) = ( cosh v cos u, cosh v sin u, v)…

Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: 4. Let f(x, y) be a function defined on a disk D not containing the origin which is given by f(r, y)…

A: See the answer below

Q: (6) I. adv, where E is bounded by the planes z=0, y = 0, =0, y+= =1 and +=1, as shown in the figure…

A: Given that,

Q: Compute the Jacobian of the map G(r, s) = (er cosh(s), er sinh(s))

A: The given function is G(r, s) = (er cosh(s), er sinh(s)). Compute the Jacobian as follows.

Q: 4.) Verify the Divergence Theorem where F(x, y, z)=(x',xz,3z) given by x' + y +z² <4. and E is the…

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Q: Show that the functions o,(x) = sin(nax²), for n = 1,2,3,..., form are orthogonal set with respect…

A: Consider the equation

Q: 1)Prove that the curves o, = {|z|=2} y 0, = {|z- i|=4} are homotypic. 2)calculate O z*dz and o z*dz…

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Q: Find the tangent plane for the level surface f(x,y,z) = 3x5 + cos (5y) + In (5z) = c at the point…

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Q: and EXPcess du dv as a function of u and v w = Xy + XZ + xz where x = u + v and y = u-v and then…

A: Use this formulas

Q: Let H be the plane 2 X- 2y- z=0 in R', that is, H={(x, y, z)eR³ | 2x- 2y- z=0} and let F be the…

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Q: Are the following linear maps invertible? a) T: R3 → R³ defined by T(x, y, z) = (y, z, x)?

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Q: Compute fS fdS for f(z,v, z) = 2y-z and S is the part of the cone 2-2+ betweenm z 1 and z 4.

A: Integration is the process of finding the anti-derivative function of a given function. The…

Q: (10) Define the metric d on R² by d( (x₁, y₁), (x2, y2)) = max{ |x₁ − x2\,|y₁ - y2|}. Verify that…

A: The given problem is to verify that the given metric d on R2. Given metric…

Q: Let F(x, y, z) = (x-1z, y¬lz, In(xy). (a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy). (b)…

A: Given Fx, y, z=x-1z, y-1z, lnxy (a) Verify for F=∇f where fx, y, z=z lnxy The gradient of a function…

Q: 4. Let f(x, y) be a function defined on a disk D not containing the origin which is given by 2.x2 f…

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: Find an equation for the tangent plane to the graph of z = xe' cos z – 2 - at the point (2,0,0). 1.…

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Q: now that the mapping a: E? ->E, (x,y) Coy, x + 2 ) is a transformaton and a collineation by finding…

A: One-One: Let (x1,y1),(x2,y2)∈E2 be such that: α(x1,y1)=α(x2,y2) so,…

Q: - Let f(z) = cosh z. (1) Find the image of S := {z = x+iye C: x < 0,0 < y < } under f.

A: Follow the steps.

Q: Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment…

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Q: 5. Verify Green's Theorem in the plane for F = (xy + y²)î + (x – y)f and the curve C is as shown in…

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Q: Let f: R → R be the function which satisfies for all (z. y, z) € R° that z cos(ry) and let C C R' be…

A: Here we have to find out line integral of function f(X,Y,Z).

Q: Find the kernel of linear map L:R R given by L(x,y,z)%3D(0,z,y)?

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Suppose we have a surface f (x,y)=x²y+cos (4x) · Which of the following is the gradient of f(x,y) at…

A: First I have found the partial derivatives of f(x,y)  with respect to 'x' and 'y' at point P(π/2,…

Q: Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment…

A: The main objective is to show that F is conservative vector field. Find the potential function. Also…

Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

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Q: Compute the Jacobian of the mapping at the given point. O(r, 0) = (8r cos(0), 8r sin(0)), (r, 0) =…

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Q: Let H be the plane 2 X- 2 y- z=0 in R³, that is, H={(x, y, z)eR³ | 2x- zy- z=0} and let F be the…

A: Given that H=x,y,z∈R3|2x-2y-z=0 And, F(x,y,z)=2x-2y-2z2y+zy-z The aim is to find F(H).

Q: (3) Suppose that T: V F is a linear map. Prove that if u E V such that u 4 Ker(T) then V = Ker(T)…

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Q: Compute the value of f.dr If F= -yi+xj and c is a from (-1,1Y to CI,1) %3D SemICirele

A: Proceed as shown below

Q: Find the Jacobian of following functions f(x,y, z) = 3xy – yz + 2y z2 - 5xyz3 g(x,y, z) = xyz -…

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Q: 2 - Find the inter val on which f are Con Cave down and infleobion Points a -y = x2 5X+10 6- ソ= (¥+…

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Q: Find the tangent plane for the level surface f(x,y,z) = 6x3 + cos (4y) + In (4z) = c at the point…

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Q: X, Y be topological spaces and f : X Y be a continuous map. If X is completely normal then Y is also…

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Q: *6. Let f: R' →R be given by =+4x'z-6xyz+4y-3x'y. Is M=f-((0}) a smooth surface (2-dimensional…

A: Given, fxyz=z2+4x3z-6xyz+4y3-3x2y2 Now, writing the given function in matrix form.…

Q: that F(x, y, z)= Divergence Theoren

A: The given vector field is Fx,y,z=xz2+12.13, sin y, x·y5. The upper hemisphere can be taken as…

Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

A: a. Suppose,  F=∇fF=∂f∂x,∂f∂y So, ∂f∂x=12x+2+tan-1y∂f∂y=x1+y2+3y2 Now, ∂f∂x=12x+2+tan-1y Integrate…