Find Vf (Gradiant f) for f(x,y, z) = ysinx + yz at p(0,1,2) Please choose one: a.(1, -1.2) b.(-1,1,0) c.(1,0,2) D.(1,0,0) to.(0,1,2)

Q: Find V. (F x G), if F(x, y, z) = 16xi +j+8yk and G(x, y, z) = xi + yj - zk.

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Q: Find fzyr. f(x, y, z) = x³y5₂6 + xy³ + yºz

A: Given: fx,y,z=x3y5z6+xy3+y6z We have to find fzyx For fzyx we first have to find the partial…

Q: Let x = (m, 1, 0,-2)", m> 0 and ||x||2 = V30, then т — Select one: а. 4 b. 7 C. 6 d. 5

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Q: Find fyx. zyx 5,6 3 f(x, y, z) = x³y2³ + xy + yºz z

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Q: If f(x, y): X 2y + 1 use the definition to find af (x, y) ду

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Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

Q: xy* Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (a4+6y8)

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Q: Q1/ If z = f(x, y) and z* - y? = 6x²y°z7 Find: and dz

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Q: Find Vƒ(P) and D7f(P). (a) f(r, y, 2) = yf + z² – 4xz; Ū = } i – $ j+ k; P(-2,1,3)

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Q: Find V x (V × F) if F(x, y, z) = xyj+ 6xyz k. V × (V × F) =

A: Given: Fx,y,z=xy j+6xyz k To find the  cross product of ∇×∇×F

Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

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Q: Find fx and fy for f(x, y) = 2x³ + x³y² + 3xy² + y ³ Select one: a. fr = 4x² + 6x²y² + 3y², = 6x² +…

A: Given function:- fx,y=2x3+x3y2+3xy2+y3

Q: Consider f(x,y) = xe*y +. Find fx , fy and fxy. y

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Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

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

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

A: Given function:To find Known facts:

Q: Find f, (8,2) if f(x.y) = e* - 5y.

A: We can find the answer as below

Q: Choose the correct answer If f(x,y)=x2+2y2, then fx(2,1) and fy(2,1) are...  fx(2,1)=5, fy(2,1)=5…

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Q: Soly

A: Given  u = ( -1 , 0, 1, 1)   v = ( 2, 3, -1, 0)

Q: Explain the Pythagoras theorem with its proof and applications. Use citation in APA format, commas,…

A: claim- explain the pythagoras theorem with its proof and applications statement- In a right angled…

Q: For the function f(x,y) = 3 x³ + 5y4 5 4 x +y find f, fy, f(-1,1), and f,(-3,2).

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Q: Let f(x, y) = x³ + y³ + 3x²y + xy + y². Find fæ, fy, fax, fry, fyy.

A: The given function is,