Let T : R → R³ be a linear dS be the sta [2 0 2] AT 37 1 2 5 4 S+S B = {(1,0, 1), (2, 0, 0), (0, 1, 1)} 1 T(v) = 3 B a + b+c=?

Q: 4) For which one of these linear maps T:R → R? is det T > 0? a) T(1, y) = (y, -r) b) T(1, y) = (x,…

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Q: Let w = f(r.0) where r and 0 are functions of s and t, then according to the chain rule is equal to…

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = √(x2 + y2 +…

A: Given: Function f(x,y,z) as follows: and a point (1,2,2) To find: Linearization L(x,y,z) of the…

Q: Let f(x, y) = xcosy- y'e*y. fry at (1,0)is equal to: %3D | -2/3 -2 1

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Q: Let g(r, y) = ye-, r(t) = In(t² + 1), and y(t) = vt. Find g(r(t), y(t)).

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let L(z, y) f(1, y) at (1, 1) . Then f-(1,1) = = y-2x +3 be the local linear approximation to O a. 3…

A: Topic:- partial differentiation

Q: If F = xi + -4yj +x2k determine the flux of F through S, where S is the portion of z2 = x2 + y2,…

A: Given - F = x i^ - 4y j^ + x2 k^  ;             S is the portion of z2 = x2 +y2 , 1 ≤ z ≤ 3 To find…

Q: Exercise 10.2 Evaluate the line integral fc(² – 2y²) ds, where C is the line segment from (0,0) to…

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Q: 3. Calculate the line integral S F - d7, where F = (x²y³, x³y?) and C is the path given by C 7(t) =…

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Q: need help evaluating this quesion pls

A: Consider the given information:

Q: t (s? + t) ds – s (s² – (s² – t²) dt = 0 %3D - 242 In Let|

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Q: Use the Chain Rule to find ôz/ðs and ôz/ôt. z = tan(u/v), u = 9s + 8t, v = 8s – 9t as az at

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Q: Consider the vector-valued function [f(x, y) xt – xy² [g(x, y) 2 Vx + y³x² [f(x, y) Which of the…

A: Find the Jacobian of the given matrix

Q: Find the linearization L(x,y,z) of the function f(x,y.z) at the given points. f(x.y.z) = e* + cos (y…

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Q: Integrate f(x.y.z) =x + Vỹ - z* over the path from (0,0,0) to (1,1,1) given by C,: r(t) = ti+tj, 0…

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Q: Integrate f(x.y,z) = x+ Vỹ - z° over the path from (0,0,0) to (1,1,1) given by C,: r(t) = t i+t°j, 0…

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Q: 3. Show that F(x,y, z) = (1+ yz) i+ (z + xz)j+ (y + xy) k is conservative. Hence find its potential…

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Q: let r1(t) = (t2, 1, 2t) , r2(t) = (1, 2, et) Compute d/dt r1(t) × r2(t)t=1 in two ways:(a) Calculate…

A: Derivative of a function is determined by change of one variable with respect to another variable.…

Q: Let F = (2z, - x, 3y): Find the flux of F, that is, - dS, where S is the graph of the function z =…

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Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=<t sin t+cos t,2t2,sin t -t cos y> Then vector is given by r→t=t sin t+cos…

Q: Let T: R2→R2 such that T(1, 0) = (0, 1) and T(0, 1) = (1, 0).(a) Determine T(x, y) for (x, y) in…

A: Given,         We have to find the transformation.

Q: Compute d/dt f (r(t)) at the given value of t for f (x, y, z) = xz − y^2, r(t) =〈t, t^3, 1 − t〉at t…

A: Given: The function fx,y,z=xz-y2and rt=t,t2,1-t, To find: ddtfrt at t=-2,

Q: Use the chain rule to find dw/dt, where w=x^5y^4+y^3z^2, x=e^t y=e^tsint, z=e^tcost First the…

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Q: Let T: R2→R2 such that T(1, 0) = (1, 0) and T(0, 1) = (0, 0). (a) Determine T(x, y) for (x, y) in…

A: Given Data T(1,0)=(1,0). T(0,1)=(0,1).   (a) Let, The general expression for the linear…

Q: 17. Integrate f(x, y, z) = (x + y + z)/(x² + y² + z²) over the path r(t) = ti + tj + tk, 0 < a < t<…

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Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: Use the Chain Rule to find dz/ðs and əz/ət. z = tan(u/v), u = 5s + 8t, v = 8s – 5t %3D az %3D as az…

A: We have to use chain rule to find the partial derivatives of z.

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = xy + yz + xz…

A: Function: f(x,y,z)=xy+yz+zx, at(0,0,0) We need to find fx,fy,fz. at the point (0,0,0)

Q: Assume that z = ƒ(x, y), x = g(t), y = h(t), ƒx(2, -1) = 3, and ƒy(2, -1) = -2. If g(0) = 2, h(0) =…

A: We use the partial derivatives to find dz/dt  Then plug x=g(t) and y=h(t)

Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

Q: let f (x, y) = x² + xy + y². Using the chain rule, calculate %3D af -(u(x, y), v(x, y)) being u = v…

A: Given that                                   f(x, y)=x2+xy+y2 And also we have…

Q: In Exercises 7–12, find the line integrals of F from (0, 0, 0) to (1, 1, 1) over each of the…

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Q: Let L(r, y) = 2y – x + 3 be the local linear approximation to f(r,y) at (1,1) . Then f-(1,1) = %3D O…

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Q: If L(x, y) is the local linear approximation of f(x, y)= x²+2y3+ 9:" at (2, 1) where g(2, 1) = 4,…

A: Given: f(x,y)=x2+2y3+g(x,y)x g(2,1)=4 gx(2,1)=4 gy(2,1)=6 At (2,1).…

Q: | Let u = x*y + y°23 where x = rse', y = rs²e=t, = 2, 8 = 1 and t = 0, by using Chain Rule. p2 Sint.…

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Q: 2. Let z = g(x, y) = e" cos y + y In(x – 1). %D Use local linear approximation to estimate g(1.99,…

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Q: Evaluate the line integral di the path over C from to Q(2,4) P(O,) where F(xy) 2xy°2+3y5 13D to ネソーメ…

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Q: 6. If u = given by x = +2, where x+y+z= 1, prove that the stationary value of u is y b a+b+c' a…

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Q: suppose that x,y,z∈R3 are such that x.(y×z)≠0. prove that x,y,z are linearly independent.

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Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: Consider ф: C" — C defined by ф(x) %3D х*. a) Kerф %3D (1,-1} b) Kerø = {i,-i} %3D с) Kerф %3D (1,1}…

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Q: If w = x²y - y²z³,x = rCost,y = rSint, dw z = re' , (r = 2)and(t = 0)then dt

A: Given equations - w = x2y-y2z3       ...............(1)x = rcost        ............(2)y = rsint…

Q: a) V = R", (x, y) = (Ax) · (Ay) where A e Mn,n is invertible.

A: Given that, V∈Rn,  A∈Mn,n is invertible matrix, i.e  A≠0 we have to show that x,y=Ax.Ay is inner…

Q: Let T : R2 → R2 given by T(x, y) = (2x + y, x − 3y), (x, y) ∈ R2. Determine [T]αα , where α = {(1,…

A: We will find the images of (1,1) and (1,2) under the linear transformation T and then write them as…

Q: Consider the following. w = xyz, x = s + 2t, y = s – 2t, z = st? (a) Find ôw/ds and ôw/at by using…

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Q: Show that F(x, y, z) = (y² – e* sin z)i + (2xy + z)j + (y – e* cos z)k is conservative and hence…

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Q: x + Y f(x, y, z) = x sin + e*% – 1

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Q: Use the Chain Rule to find ôz/ðs and dz/dt. z = tan(u/v), u = 3s + 6t, v = 6s – 3t dz %3D as Ot

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