Given f(2, y, z) =v V-I - 2y + z, find f.(z, y, z) = f(z, y, z) = f(1, y, z) =

Q: Let f = zy + yx, v = [y, z, 4z - x], w Find - [vª, zª, x®]. (a) grad f and f grad f at (3, 4, 0) (b)…

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Q: Find ôf af of and дх ду dz f(x, y, z) = 3×EYZ + 7yexz af -7 Əx af 7 ду af 3xe"y + 7yex %3D X ze

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Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

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 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: 2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer…

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Q: Find V x F for F(x, y, z) = -IZ -yz √₁² + y²² + √²² +2²² =j + √√x² + y²k.

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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 the linear approximation of given function at (0, 0). 3x + 4 2y + 1 f (x, y) = f(x, y) =

A: We have to find the Linear approximation of the given function.

Q: Q1 If f(x,y, z) = 2 x²y + ez+ Vz Inx %3D Find fr fy and f2

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Q: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

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Q: Let F(z, v)-v +y+3z+1-0

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Q: 1 f(v) = , sec vtan v, F(0) = 4, 3 <V<-

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Q: f(x, y, z) = xyz + xy3 + yz3 + zx3 %3D fy

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Q: Let F(x, y) =x2+xyz+z , find at the point (1,1,1)

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

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Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

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Q: Find fzyz. f (x, y, z) = x°y°z° + xy7 + y®z f zyz ||

A: Using derivative,

Q: Maximize the function f(x, y, z) = x² – y², given that x² + 2y² + 3z² = 1. %3D

A: Here, we can use Lagrange multiplier to maximize f(x,y,z)=x2-y2 with constraint x2+2y2+3z2=1. Let…

Q: Find the linear approximation to f(x, y, z) = at the point (2, –1, –2): f(r, y, z) z

A: A Givenfx,y,z=xyz at the point 2,-1,-2linear approximation at the point…

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: Find a function f (x, y, z) such that ∇f =〈z, 2y,x〉.

A: Given that, ∇f=z,2y,x We have to find a function f(x, y, z) such that ∇f=z,2y,x. Let us consider,…

Q: Find Vf at the given point. f(x,y,z) = x² + y² - 4z²+zlnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k…

A: Topic:- application of derivatives

Q: u,v) = ve*tv, and z(u,v) = (u+v)cos v?. OG nd and by using multivariable Chain Rule method. du u=1

A: Given: Gx, y, z=e2x+y+3zxu, v=u lnu+vyu, v=veu+vzu, v=u+v cos v2  To Find: To find  ∂G∂uu=1v=0  and…

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

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Q: Calculate ∬S f(x,y,z) dS For y=2−z^2,   0≤x, z≤7;    f(x,y,z)=z

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Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

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Q: f(x, y, z) = e-3zyz 三 fy = 三 ニ f.

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Q: Find f, (x,y) and fy (x.y), and explain why f(x,y) has no local extrema. f(x.y) = 8x + 3y + 4. fy…

A: It is partial derivative

Q: Let f(x, y) = xcosy- y e*y. fxy at (1,0)is equal to:

A: For finding the Partial differentiation we need to take one variable constant and differentiate the…

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: If f(x, y, z) = ln(æª + y!0 + z®) + V(x10 + y8 + zª), then find fr, fy and f; at (1, 1, 1).

A: Given, f(x,y,z)=ln(x4+y10+z8)+(x10+y8+z4)

Q: Calculate fw(-1, 2, 0, –1) where f(x, y, z, w) = xy²z – xw² – e2a²-v²-²+2w²

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Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

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Q: (e) 3x E R, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0.

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Q: Find the linearization of f (x, y, z) = xy / z centered at (2, 1, 2). Use itto estimate f(2.05, 0.9,…

A: Our Aim is to find the linearization of f(x,y,z) =xyz centred at (2,1,2).and then using that value…

Q: Let f(z) = 5z2 + 4z.  Find u(x,y) if z = 9.6 + 2.9i .

A: Using , complex function properties

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…

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Q: Let F(x, y, z) = x³yz² – 6x?yz + 9xz – 5y°z. Find F %3D xyz Fxyz

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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: Use the linear approximation of f(æ, y) = e+y at (0, 0) to estimate f(-0.03, -0.03)

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Q: Find the linear approximation to f(x, y, z) = " at the point (2, –1, 1): f(x, y, z) =

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Minimize f(x,y,z) = x + 2y + 4z subject to the condition ** +y“ +z* = 7

A: Hello, thanks for your question .According to our policy I m doing the very first question . Please…

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

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Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

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Q: X+Z+3Siny X +2y-2

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Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

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