Find u x v, v x u, and v x v u = i+j, v-j-k (a) ux v (b) v xu (c) V X v

Q: Find x, y e lº such that || x || ∞ = 1 = || y || = || x+y 2 || x #y.

A: As per the question we have to find two sequences x, y from the norm-space l∞ such that : ||x||∞ = 1…

Q: x+y If Z = x.n. f (***), then show that: X. Zx + y.Zy = z

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Q: Q. Let a = x1 dx2 + x3 dx4, B = x1 ×2 dx3 dx4 + X3 X4 dx1 dx2 and y = x2 dx1 dx3 dx4 be forms on R4.…

A: given  α=x1dx2+x3dx4 , β=x1x2dx3dx4+x3x4dx1dx2γ=x2dx1dx3dx4 calculate  (i) αβ , αγ…

Q: = f(x,y, z) = x + sin y and Calculate if w ди x = x(u, v) = In (u + v), y = y(u, v) = e".º and z =…

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Q: Find (a) u x v, (b) v x u, and (c) v x v.

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Q: II. r*yz dxdydz K = {(x. v. z) : 0<x<1, 0 <y<r. 0<z<z°u}

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Q: 3. Find V x F for F(x, y, z) = -IZ i+ x² + y² -yz 1² + y² +√x² + y²k.

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Q: find all values of x and y such that f.(r, y) = 0 and f,(x, y) = 0 simultaneously.

A: Partial derivatives of the function is differentiating the function with respect to only variable…

Q: Find u x v, v x u, and v x v. u = 5i + 9k v = 2i + 9j – 4k. (a) U X V (b) (c) v x v

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Q: Find V (V x F), if F(z, y, =) = 3e""i+7ze'j – 3e"k. V. (V x F) =

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Q: Find u x v, v x u, and v x v. u = i -j- k, v = 2i + 2j + 2k (a) u x v (b) V x u (c) V X V

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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: 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: Find V. (F x G), if F(x, y, z) = 3xi +j+ 10yk and G(x, y, z) = xi + yj – zk. - V. (F x G) =

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Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: If f(x, y) = In(4x + y) then: V f(x, y) = i+ j

A: To obtain the gradient of the vector

Q: Find V x (V × F) if F(x,y, z) = 8xyj+ 4xyz k. V × (V × F) = (4(y+2), 4:x, 0)

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Q: u = x² + y³ + z*, X = s•t = s2 +t2 y = z = s-t

A: We find complex function

Q: Find V (F x G), if F(x, y, z) = 13xi +j+ 7yk and . G(x, y, z) = xi + yj - zk. V. (Fx G) =

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Q: Find u x v, v x u, and v x v. u = 3i + 7k v = 5i + 9j – 3k. (a) u x v (b) V Xu (c) V X V

A: Given query is to find indicated cross product.

Q: Evaluate f(х, у) ds. f(x, у) %3D у + 3 s: r(u, v) = ui + vj + 4vk, 0 sus 1, 0svs 4

A: Given: fx,y=y+3 S:ru,v=ui+vj+4vk, 0≤u≤1, 0≤v≤4 Differentiating r with respect to u, ru=1,0,0…

Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

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Q: Find u x v, v x u, and v x v. u = i + j, v =j + k (a) ux v (b) v x u (c) v x v

A: We will find out the required values.

Q: Find u x v, v × u, and v × v. u = 6i + 8k v = 3i + 8j – 4k. (a) u x V (b) (c)

A: This question is based on cross product.

Q: b. f:R² → R defined by f(x, y) = x² + y². Find f-1(0), f-'(1), and f-1(U), where U = (1,4). %3D %3D

A: Given data:     The expression of the function is: f(x,y)=x2+y2.     The expression for the inverse…

Q: Find u x v, v × u, and v x v. u = 2i + 9k v = 4i + 6j – 3k. (a) UX V (b) (c) V X V

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Q: (h) Vx E R, 3y E R, (x + y > 0 or x + y = 0). (i) Vx E R, 3y E R, (x + y > 0 and x + y = 0). (j) (Væ…

A: .

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: Prove ¬(3x € X : (Vy ¤ Y : E(x, y))) = \x € X : (‡y ¤ Y : ¬E(x,y)) (Vx X: (³y € Y : E(x, y))) = (3x…

A: We have to prove  a) ¬∃x∈X : ∀y∈Y : Ex, y=∀x∈X : ∃y∈Y : ¬Ex, y b) ¬∀x∈X : ∃y∈Y : Ex, y=∃x∈X : ∀y∈Y :…

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

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Q: f(x, y) = iy² – x², P(1,4), v = 2i + j

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Q: ху af If f(x,y) then is %3D x2+y ax

A: Given function,  fx,y=xyx2+y

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i − j − k, v = 2i + 2j + 2k

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Q: Find V (F × G), if F(x, y, z) = 11xi+j+3yk and G(x, y, z) = xi + yj – zk. V. (F x G) = %3D

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Q: Find V· (F x G), if F(x, y, z) = 10xi +j+7yk and G(x, y, z) = xi+ yj – zk. V · (F × G) =

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Q: 2. True or False a. Vx E R, x² > 0 b. Vx E R, 3n EN, x" > 0

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

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: I| f(x, y, z) dV, E = {(x,y, z) | 0< x< v2, x < y < V4 – x², 0 < z < x² + y² + 8} %3D E

A: Question 3. Given integral is ∫∫∫Efx,y,zdV, E=x,y,z/0≤x≤2,x≤y≤4-x2,0≤z≤x2+y2+8 It has to find the…

Q: Maximize utility U(x, y, z) = 24yz +16xy +16xz Subject to G (x, y, z) = xyz= 384

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Q: Find real numbers x, y and z such that (а) (b) 7xi + (y – 3)j + 6k = 10i + 8j – 3zk (x + 4)i + (y–…

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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: Find V· (F x G), if F(x, y, z) = 6xi+j+15yk and G(x, y, z) = xi + yj – zk. V · (F × G) =

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

A: Let's find.

Q: Find V (F x G), if F(r, y, z) G(x, y, z) = xi+ yj - zk. = 2xi +j+ 8yk and V. (F x G) =

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Q: 3. r/s*t/u- v + w * x - y++

A: Given expression is, rs*tu-v+w*x-y++

Q: Q.1. (b) If u(x) = 4x – 5 ,v(x) = x² and f(x) == then find: %3D %3D %3D f(v(u(x)))

A: Given: ux=4x-5, vx=x2 and fx=1x To find: fvux

Q: Find V· (V × F), if F(x, y, z) = 7e*²i+ 6xe"j –- 6e²k. V·(V × F)

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Q: Find u x v, v x u, and v x v. u = i +j, v= j - k (a) ux v i+j-k (b) v x u -i+j-k (c) v x v Oi + Oj +…

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Q: Find u x v, v x u, and v x v. u = 3i + 7k V = 4i + 8j - 2k. (a) u x v (b) (c) V X V

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Q: Find V (F x G), if F(x, y, z) = 11xi+j+13yk and G(x, y, z) = xi + yj – zk. %3D V. (F x G) =

A: Given,            Fx,y,z=11xi+j+13yk and Gx,y,z=xi+yj-zkTo find : ∇·F×G