5. If 3x²z+y³-xyz³ = 0, find az / əx. 6. Show that if w=f(r-s,s-t,t-r), then dw dw dw dr + + = ds ôt = 0.

Q: If the substitution u = √x + 1 is made, the integral 3 A S u² u² - 1 du B du 3 2u²2 u² - 1 √ √x+1 dx…

A: We solve the given problem by using the substitution method.

Q: 2. (у? — 2ху + 6х)dx — (х? — 2ху+ 2)dy %3D 0, whenх%3D 1,у %3D2 = 3. v(2uv? — 3)du + (3и?v? — Зи +…

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Q: 3. zy if y + x² – 3xz = 222

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Q: Suppose that u · (vxw) = 47. Find u. (wxv). u. (wxv) = i

A: Given: u·v×w=47To find:u·w×v

Q: d (3y? + 4y +2 Find dy y

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Q: 2. For x 2 0, which equation is false? 3, 2 (x) = V3 А. X2 %3D B. (x³) = Vx3 c. (x) = Vx3 ( = С. X2…

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Q: Suppose that u × v = ⟨1,0,4⟩. Find (2u−3v) × v.

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Q: Sv.Vdxdy = dxdy = ду 2 + JR V.(6,x)-V,(b,x)]áx + [ [7 (a, y) –V,(0,v)ky.

A: Here is the solution of the given problem.

Q: Find aw av aw - dv 2 y when u = 0, v = 0 if w = x² + x₁ x= u=0, v=0 +,x=6u-5v + 1, y = 6u +2v-6. X…

A: Given that w=x2+yx, x=6u-5v+1, y=6u+2v-6. We have to find the value of ∂w∂v when u=0, v=0.

Q: Let U(z, y) (2x +3)(y+5). %3D Select the correct expressions for Uz and Uy: (A). Uz= 2x+3. %3D (B).…

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Q: Let F(x,y,z) = 3x²y + 6y³ – 5xz². Find VF ,V²F¸ K×VF, and V×VF.

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Q: Consider the differential dz 2.ry da + (x² + 2y) dy. (11.39) %3D Evaluate the integral S2 dz along…

A: The integral, ∫(x1,y1)x2,y2dz=∫(x1,y1)x2,y22xydx+(x2+2y)dy∫(x1,y1)x2,y2dz=∫(x1,y1)x2,y2Mdx+NdyWhere,…

Q: use Lagrarge mul tipliers Sublect to the Constcair t to mekim,ze x+2y=5

A: Consider the given information. fx,y=x+4xy+6y and x+2y=5 Now, make the auxiliary function.…

Q: 7. Solve: dy x + 3y d.x 3x + Y

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Q: +3. . Find the linearization of _9). Can you tell anything about the error? at (3,2). Evaluate at…

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Q: 4.83. Show that dz z²a² 2a In ( ² = a) + ² th-¹2+ a +C₁=-coth a C2.

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Q: 8. Let a2 + xy³ + 2x = 11. Find y"(x) at the point (1, 2). %3D

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Q: If WX = 3t - 45 and VY = t, what is Y? W V Y こ

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Q: Calculate Jazyz if Ax,y,2) = 5x³ + 7x²y³ + 2y³ + 2z³. O A frzy: = 5x2 - 7xy O B. frzy2 = O C. None…

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Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 5xyz k. V x (V × F)

A: Given function is F→x,y,z=9xyj^+5xyzk^. To find:  ∇×∇×F→ Concept: Cross product formula for given…

Q: Let f(x,y) = In ( x2 + y). If fy(2,a)=fy- 1, 2), what is the value of a? а. 3 O b.7 О с. 8 d. 6 O e.…

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Q: (xy ☺ Ty 5. Tyy Ty x 7) Tz ® Tzz 6. TzX

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Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

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Q: iv) if z = (xy)¯1 then zx – Zy = %3D b.x + y c. z?(x – y) d.z²(x + y) a. x – y

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Q: Suppose u = (4, 1, 1) and v = (–4, −1, −3). Then: u + v= Ա υ V= u= 2u= -1/v= 7u - 6v=

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Q: uppose that x + y = 2. What is y" at the point (1, 1)?

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