Find u · (v x w). (4, 4, 4) (4, 6, 0) w = (0, 0, 9) u = V =

Q: Find g(u(x, y), v(x, y)) if g(x, y) =ysin(x2y), u(x, y) =x2y3 and v(x,y)=πxy.

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Q: Find R f(x, y) dA where f(x, y) SIR f(x, y) dA- = x and R = [0, 4] × [-2, 4].

A: Given f(x, y) = x and R = [0, 4] x [-2, 4]

Q: f(x, y, z) = 4xy-8xyz + 7yz2 %3D (x, y, 2) = %3D x, y. 2) = %3D x, Y, 2) = %3D

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Q: If f (2, y, 2) = r'yz + 23 then fyzæzzaz (-1, 1, 1) %3D

A: The expression fx is the partial derivative of f with respect to x. When partial derivative is…

Q: Suppose that V f p = (2, -4, 4). Is f increasing or decreasing at P in the direction v = (2, 1, 3)?

A: Given ,  ∇fp=2,-4,4    v=2,1,3

Q: f(x, y) = xy, x = 1 - √t, y = 1 + Vi

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Q: f(x, y, z) = 3x²y - 5xyz + 7yz2 2. f,(x, y, z) = f,xx, y, z) = f(x, y, z) =

A: Given query is to find the partial derivative for the given function f(x,y,z).

Q: Find f, (x,y) and f, (x,y). Then, find f, (3, - 4) and f, (4, - 3). f(x,y) = - 7xy +6y +3 fx(X.y) =

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Q: (d) u =-,v = xy, = a' ху, 21

A: Consider the given information. (d) Consider the given values. u=12-12x2v=xy The equation of the…

Q: f(x,y,z) = xy + yz + zx, (2, - 2, - 1), A = 3i + 2j - 6k

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Q: zy? (z, v) + (0, 0) f(x, v) (z, u) = (0, 0) %3D

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Q: Q.2: Find u x v, where a: u = (1,–3,4) & v = (3,4, 7), ats b: и %3D (1,2,3) &v %3D (1,5, 2).

A: Given: a u=1, -3, 4 and v=3, 4, 7b u=1, 2, 3 and v=1, 5, 2 To Find: u×v=?

Q: Find u x v, v × u, and v × v. u = i - j, v=j - k V (a) u x v (b) v x u (c) v x v

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Q: c) Find u (v x w) if u = [0,0, p], v = [0, q, 0] and w = [r,0,0]. %3D

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Q: f(x, y) = (-x – 2y, x – 4y).

A: Follow the steps.

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: F = [r. -x, 0]. = [y. -X, S: 3r + 2y + := 6, x2 0, v 2 0, z 2 0

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Q: x = u - v2, y = u + v (x, y) = (u, v)

A: Given , x = u - v2 , y = u + v

Q: X > U (M-, M+) M, Xca) 3. X(2) rimators: 2 1x

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: uxx + uyy =0, 0<x<a, 0 <y<b, B.C. u(x, 0) = 0, u(x, b) = f(x), 0 ≤ x ≤ a, ux(0, y) = 0, ux(a, y) =0,…

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Q: find the distance d(u, v) between u and v in the given exercise.

A: We need to find the distance between the two vectors.

Q: A) f(x,y,z) = 2x + y – z , Q = {(x, y, z): 0 < x, z < 2,-2 < y< 2}

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

Q: af Find if f(x,y) = ysin xy

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Q: Find ||u||, ||v||, and ||u + v||. u = -2, V = 5, (a) ||u|| (b) ||v|| (c) ||u + v||

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Q: If F (x,y,z) = x²z +elx xy², find (a) V(F + G) and (b) V(FG) at the point (1,0, -2). and G(x,y, z) =…

A: Given Fx,y,z=x2z +eyx      and   Gx,y,z=2 z2y-xy2

Q: f(x,y,z)=x+y+z and r(u,v)= (2u+ v, 3u - v, u+2v). What is the value of f(r(u,v)) r, xr, AA when u=2,…

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Q: b) If x = u(1 + v) and y = v(1+u), find vx, Ux and a(u,v) a(x.y)

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Q: 27. F(x, y, z) = x'y – y°z², v = (-1,7, 3), P = (1,0, –1

A: F(x,y,z)=x2y2-y2z2

Q: f(x, y, z) = 2 ≤ x ≤ 10,0 ≤ y ≤ 4,0 ≤ z ≤4

A:

Q: If f(x.y,z)= y + xz then f ,(1,1,1) =

A: The given function is  f(x, y, z) = y5 + xz

Q: g(x, y, z)

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Q: A v xu u = (1,3,-3), v = (4,0.2) T......

A: Let's find.

Q: Let f(x, y, z) 48 Then Vf = and Duf(2, 1, 3) in the direction of (2, 1, 2) is

A: This is gradient of f in which take all first order partial derivatives.

Q: Vy + z f(x, у, 2) 3 (а) f(1, 5, 4) (b) f(6, 7, –2)

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Q: f(x,y)= exsin (y), fx(x,y)

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Q: (x, y, z) = ( i i

A: Given that Length of vector = 6√3 We have to find component of vector.

Q: Determine D,f (4,-1,6) for f(x,y,z) = ery + 4zx in the direction of (-3,2,6).

A: Given fx,y,z=ex2y+4zx3 in the direction of -3,2,6

Q: x (u, v) = (u – v² ², u² + 1, v²) %3| |

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

Q: Find projy u. v = 7i-3j+ k, u = -4 j+ 3 k 60 45 j+ k 59 59 O 105 i- 59 45 15 k 59 59 9 9. +k

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Q: Find u × v, v × u, and v × v. u = 4i + 8k v = 4i + 8j – 4k. (а) ихv (b) v × u

A: We have to find

Q: (a) F(r, y, 2) = 7+ 27 + 3K. (b) F(r, y, 2) = i + 25 + zk. (c) F(r, y, z) = xỉ+ yj+ 3K. (d) F(r, y,…

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Q: Find f'(2) where f(t) = u(t) v(t), u(2) = (1,2, –1), u'(2) = (3,0, 4), and v(t) = (t, t2, t).

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Q: Find V. (V × F), if F(x, y, z) = 2e*i+ 6xej – 7evk. V. (V x F) =

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Q: Find V. (V x F), if F(x, y, z) = 6e"²i+ 2xe³j – 3ek. - V·(V × F) =

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Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -2), u'(3) = (4, 0, 7), and v(t) = (t, t², t³).

A: Introduction: The outside-inside rule, composite function rule, and function of a function rule are…

Q: Evaluate fcF. dr where F = ( 3 z – y)i + (2 x +2 z)j + 2 z k along the straight line from (1,1,2) to…

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Q: f(x, y, z) = 4x²y - 2xyz + 9yz2 (X, y, z) = ,(x, y, z) = f_(x, y, z) =

A: Answer and explanations is given below...

Q: Find Cov(X, Y)

A: Covariance: It is a statistical measure used to establish a relationship between two random…

Q: z = f(x, y) = r* – x²y+ 4y, r= g1(u, v) = u² + v², y = 92(u, v) = = uv.

A: Let's find.

Q: 2. f(x, y, z) = exyz² Find fxyz

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Q: et V xu u = (1,3,-3), v = (4,0,2) e l -3 %3D ......

A: Given:            u=1,3,-3            v=4,0,2 The cross product of two vectors is…