2² – 5y? Then y² + 2z2 Let f(x, y, z) = fz(æ, y, z)= | fy(æ, y, z)= | f:(x, y, z)=

Q: x = g(t) , y = h(t) , z = f(x, y) , g(3) = 2 , g'(3) = 5 , h(3) = 7 , h'(3) = -4 , fr(2,7) = 6 ,…

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Q: In Exercises 23–27, find ƒx , ƒy , and ƒz .

A: You have asked multiple unrelated questions in the same post. I have addressed the first question.…

Q: (xy(x²-y²) Let f(x, y) =} (x²+y²) (x, y) ± (0,0)| show that fxy (0,0) + f yx(0,0) (x, y) = (0,0)

A: This question is taken from the partial derivative in which we have to prove the given statement. We…

Q: Find fzyæ. f(r, y, 2) = a'y"2³ + xy® + y°z %3D f zyz

A: Given f(x,y,z)=x^4y^7z^5+xy^6+y^7z

Q: Find fr, fy, and fz. f (x, Y, z) = z In(x°y²cos(52)) fa = fy = fz = ||

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Q: f(x, y) = /2x – y /2х — у f(x, y) = In(9 – x² – 9y²) f(x, y) = /1 – x²? - VI – y² S(x, y) = Vy + /25…

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Q: D. f(x, y, z) = 1x + 10y + 8z Vf(x,y) =i+j+k E. f(x, y, z) = 1x² +10y² + 8₂² ▼ f(x, y, z) =i+j+k

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Q: 1. Consider the function f(x, y, z) = x² + 2y + 2², which is differentiable at (2,1,1). 1) find…

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

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: Find fzyæ. f (x, y, z) = x°y®°z° + xy° + y°z f zyr ||

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Q: xy(x² – y²) if (x, y) # (0,0) Let f(x, y) x2 + y? Show that fi(0, y) = -y for if (x, y) = (0,0) all…

A: Here, the given function is: f(x,y)=xy(x2-y2)x2+y2, if x,y≠(0,0)0                  , if (x,y)=(0,0)…

Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: 2x – 5y (1, y) # (10, 4) Find C so that the function f(x, y) = V2r – 5y +4 – 2 C (x, y) = (10, 4) is…

A: Given function is fx,y=2x−5y2x−5y+4−2, x,y≠10,4C                        , x,y=10,4 Given function…

Q: Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

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Q: z – 1 ive of f(z) = Leave your ans %3D z +1

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Q: Let f(x, y) be differentiable at (ro, yo). Then we have f(xo + Ax, yo + Ay) - f(xo, y0) fa (ro, yo)…

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Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

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Q: If f (x, y) = V3+ y³ In (x² + y³)ešin(zy+y*) + x² + 10y.then fz (1,0) = %3D

A: We need to differentiate the given function partially w.r.t x. The given function is: f(x,y)=x3+y33…

Q: azz 2. A. If z = sin(3x+2y) , verify that 2 - 3 a2z = -6z ay2 B. If f = x³y³ + 2xcosy + y² lnx then…

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Q: Find fzya. f (r, y, 2) = x°y*z" 5.8 + xy* + y°z %3D f zyz

A: Given data÷

Q: . Let f(x,y) = 10xy^4 +x^5y^2. Find fyyy.

A: We have to find solve

Q: 0.4 at r 3, use linear approximation to estimate Ay Let y = 4x² + 6x + 2. If Ax |3| Ay =

A: Given y=4x^2+6x+2

Q: 3) Evaluate f.(y + z)dx + (x + z)dy + (x + y)dz, C consists of line segments from (0,0,0) to…

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Q: Find fæ, fy, and fz. 4.5 f (x, Y, z) = 4z In(x*y° cos(5z))

A: To find the partial derivatives with respect to x ,y ,z.

Q: Find fz and fy- f(z, 9) = [" 9eª dt f.(x, y) = f,(x, y) =

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Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(5) = 8, g'(5) = 9, h(5)…

A: Given that z=fx,y, where f is differentiable. Here, x=gt and y=ht. Also, let, g5=8, g'5=9, h5=-7,…

Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

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Q: 11) S(x,y) = fg(1)dt, Ans. f. =-g(x), f, = g(y) (g continuous for all ?) 12) f(x, y,z) =1+xy² – 2z²…

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Q: 7. f(x) = x² In x, f"'(x) 1 8. y = -, y" 1 .f"(q) 9. f(q) = 2g* 10. f(x) = /x, f"(x) 11. f(r) = /9 –…

A: The objective of the question is determine the derivative of the given function "y".

Q: 2² – 6y? Then Let f(x, y, z) y2 + 4z² fz(x,y, z)= fy(x, y, z)= f-(x, Y, z)=

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Q: 2.2 11, IfF = xyz\+x*y°z}+ xyz k then find div F at (2, 1, – 3).

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Q: 114 f(x, y) = (xy²-1 y-1 tion f(x, y) at the point (1,1), where (x, y) = (1,1) (x, y) = (1,1)

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Q: (8) Fs [ J" f (x, y) | бул 1 = d^Fs dyn proof (H⋅w-)

A: Introduction: A Fourier remodel (FT) is a mathematical remodel that decomposes capabilities relying…

Q: Find fr and fy. 2e" dt f (x, y) = 2, f.(r, y) = f„,(x, y) =

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Q: Let f(x, y, z)= = fz(x, y, z)= fy(x, y, z)= fz(x, y, z)= 2² - 2y² I y² + 4z² Then

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Q: 1) Consider (x, y, z) = 2xyz - x²y³ v(x, y, z) = xy² + y sin(z) F(x, y, z) = F₂(x, y, z)i + F₂(x, y,…

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Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

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

Q: (a) If F(v² – x²,v² – y², v² – z²) = 0 where v is a function of x, y,z show that 1 dv 1dv 1 dv 1 хдх…

A: Using chain rule.

Q: Display the values of the functions in Exercises 37–48 in two ways:(a) by sketching the surface z =…

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Q: f (x, y, z) = x² + y² + z² and u = (1,0, 1) at P(1, 1, 1).

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Q: If f(x, y, z) = In(x +y+z) then f:(1,0,0) : %3D

A: Given that :-    f(x,y,z)=ln(x+y+z) find out :-   fz(1,0,0)=?

Q: Find fx, fy, and fz. f(x, y, z) = In (xy) Z fx = z ln: fy=z In :f, = In (xy) fx :수:fz= In (xy) fx fy…

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Q: 1. f(x, y) = 1- x - y 2. f(x, y) = xy 3. f(x, y) = Vx² + y² 2

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Q: 2xy F(x, Y) =Vx+ 2y (1, 1) f,(x, y) = 1,(1, 1) S(1, 1)

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Q: If f(x, y, z) = In(x° + yº + 2®) + v(x° + y8 + z®), then find f, fy and f; at (1,1, 1). %3D

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Q: f (x-y/x)=(y/z) then z=[x(z-y)]/y

A: Given that, x-yx=yzz=xyx-y         ...(1)

Q: xy Let f (x,y) =In Then f „(1,- 1) =.. %3D 3x2+4y3 XX

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Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

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Q: 15. f(x, y, z) = xy + yz + zx, Po(1,-1, 2),u= 3i + 6j - 2k

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Q: ntegrais. I, da, D= {(x.y) 0sxs20sys2% dA, D = x +2 [['e"d4, D={(x,y)| 0s ys 4,0sx<y}

A: Double integration