Let u = (2, 1, – 1) - (-4, α + β 2) w- (α, 0, β ) Find the values of a and ß such that u is parallel to v and v is perpendicular to w

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y). =1 a(x,y)'a(u,v)

A: Given x=u1−v and y=uv We have to verify ∂u,v∂x,y⋅∂x,y∂u,v=1 Solve x=u1−v and y=uv for u and v, we…

Q: ủ (u x) = 0 for all u, v in R.

A: We will prove whether this is true or false as following.

Q: Use the chain rule to find where g(u,v) = f (x(u,v),y(u,v)), f(x,y)=xy³ -4x² , ög ди x(и, у) -и*…

A:

Q: Use the method of separation of variables to solve: (ôu ôu - = 0 in (0,1) × (0,+∞), (2) u(0,t) =…

A:

Q: Let f(x,y) = x² – xy+y² – x. Find the direction u and the value of Duf(1, – 1) for which Duf(1, – 1)…

A: We have to find maximum directional derivative.

Q: Find u x v, v x u, and v X V. u=i-j, v=j-k

A:

Q: Find (u, v), ||u||, ||v||, and d(u, v) for the given inner product defined on R". u = (5, 0), v =…

A:

Q: дz For z = x² + xy³ ; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 Əw

A: z=x2xy3, x=uv2+w2, y=u+ve2at u=2, v=1 and w=0, x=2×12+0=2y=2+1e0=2

Q: 2) Find Ow/du and ow/ov for w=xy+ yz + xz, x=u +v, y=u-v, z = uv at the point (u, v)= (1/2,1). 3…

A:

Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Verify that x − p is orthogonal to p.

A:

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

A:

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…

A:

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y)_1 a(x,y) a(u,v)

A:

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…

A:

Q: 2) Let u(xy,2) = でさす。R。 () Find He(tいり, "g(1,0,り、 Uy(1,0,1). ニ0. (k) Show that oty a22

A:

Q: 2: Show that a map T is linear if and only if T(Au + v) = XT(u)+ T(v) for all A ER and vectors u, v.

A: A linear transformation satisfies  T:U-V  Then T(u+v) = T(u) +T(v)          T(au) = aT(u)  For all a…

Q: of at (x, y, z) = (2, 3, 4). ay Let f(x, y, z) = (x + y)z. Evaluate

A: Given :fx,y,z = x+yz

Q: Let w = x +y+ z, x = u³ + v³, y = eu, z = u – v and u = t+1, v = e*. Find the value of w (0). %3D…

A: Given: To find: The value of w'(0).

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y). -=D1 a(x, y) a(u,v)

A:

Q: Find g(u(x, y), v(x, y)) if g(x, y) = y sin(xy), u(x, y) = x²y', and v(x, y) = Txy. %3D

A: We have given g(x, y)=ysin(x2y), u(x, y)=x2y3 and v(x, y)=πxy. To find gu(x, y), v(x, y), first…

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the fol u(-3, 6) = 1…

A:

Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

Q: Integrate f(x,y,z) = x+ Vy -z° over the path from (0,0,0) to (3,9,3) given by C,: r(t) =t i+tj,…

A: The given function is, Let, Also the given paths are, So,

Q: Let V R2, W1 = {(x,0) : x E R}, W2 = {(0, y) : y € R}, and W3 Prove that V =W1 W2 = Wı W2 = W2 W3.…

A:

Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).

A: The linearization of a function f(x,y,z) at a point (a,b,c) is given by the expression;…

Q: Find r' (2), where r(t) = u(t) × v(t), with u(2) = (1, ,2, – 1), u' (2) = (3, ,0, 4) , and v(t) =…

A: Solution :-

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: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: To find the linearization Lx,y,z of the function at the given points fx,y,z=x2+y2+z2 at 1,0,0

Q: Given z=x^3+xy^2,  x=uv^3+w^2,   y=u+ve^w then find: ∂z/∂u when u=−1, v=−2, w=0u=-1, v=-2, w=0

A:

Q: (a) express ∂w/∂u and ∂w/∂y as functions of uand y both by using the Chain Rule and by expressing w…

A: The given question should be (a) express ∂w/∂u and ∂w/∂v as functions of u and v both by using the…

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

A:

Q: If L(x, y) is the local linear approximation of f(x, g(2, 1)= 4, g,(2, 1)=4 and g,(2, 1)=6, then L O…

A: Use formula of linear approximation

Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

A:

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…

A:

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

A:

Q: Find the Jacobian a(x, y, z) (u, v, w) for the indicated change of variables. If x = f(u, v, w), y=…

A: Find the corresponding derivatives and then find the determinant

Q: 2) Find Ow/ôu and ôw/ôv for w= xy+ yz+ xz, x=u+v, y =u –v, z = uv at the point (u, v)= (1/2,1). 3…

A: If w=f(x,y,z) and x=g(u,v) ; y=h(u,v) and z=t(u,v) then, ∂w∂u =∂w∂x.∂x∂u+∂w∂y.∂y∂u+∂w∂z∂z∂u  and…

Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i %3D Duf = i

A:

Q: Let r E R and --(), v- (), -- (1). 3 u = V = W = 2 For which values r ER is the set {u, v, w}…

A:

Q: b) Suppose to i that and V х-у Calculate the x and and y by and Jacobian ð (u, v) 2 (x, y) hence…

A: Suppose that x and y are related to u and v by…

Q: J f ds if Evaluate Of(x, y, z)=x+y, and C is the combinations of lines connecting adjacently the…

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

Q: Let u = (1, 1), v = (3, -2), w = (4, 3), and y = ( map from R² -3, 4). Let L be a linear | to R?…

A: We know Let  Given

Q: Let f(x,y) = x² + xy- y² – x. - x. Find the direction u and the value of Duf(1,1) for which Duf(1,1)…

A: According to question we need to find for (x,y) = (1,1) So, I am assuming there is a typo in options…

Q: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

A: Given: u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). And, (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

Q: Given: z = a* + æy², x = uv* + w*, y=u + ve" az Find when u = - 2, v = 2, w = 0 dv

A: To find: The value of ∂z∂v, when u=-2, v=2, w=0. Given: The values are z=x4+xy2, x=uv4+w3 and…

Q: Suppose that we have n independent observations (X¡, Y¡) pf the random vector (X, Y) with pdf f(x,…

A: Hello thank you for the question. According to our honor code can answer only three sub parts at a…

Q: Integrate f(x,y,z) = x + √√y-z² over the path from (0,0,0) to (4,16,4) given by C₁: r(t) = ti+t²j,…

A: