y Let f(x, y) : Compute f-(7, –2), fy(7, –2) and fæy(7, –2). x + 3y

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: (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 a function f(x, y, z) such that Vƒ = (3z, 4y°,3x).

A: Given that :-       ∇f=3z,4y3,3x  ⇒∇f=3zi^+4y3j^+3xk^  ....(1) Now we know that…

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

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Q: Let f(x, y) be a function such that F(s, t) = f(s – 2t, t²) fx(2, 1) = 5, fx(0, 1) = 3 fy(2, 1) =…

A: Here F is function of s,t and s,t and function of x and y  So we first differentiate with respect to…

Q: Consider the function f (x, y, z) = x² + y – xyz Find grad

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Q: Find the linearization L(X,Y) of the function  f(x,y)=y-1/x+1 at(0,0).

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

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Q: Evaluate f fs 2² dS, where S is the portion of x2 + y² + z² = 2 in octant 1.

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Q: Find the linearization L (x, y) of the function f (x, y) = y/-x at (-9,4). 2 L(x, y) -x+ 3y – 6 3…

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Q: Evaluate f(x, y, z) dV for the specified function f and box B. f(x, y, z) = z3; 13 x < 8, 1 S ys 5,…

A: Given

Q: Find fr, fy, and fz. f(r, y, 2) — вуzIn(4ry) fz fy f: =

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = (x + y + 2)2 at a. (0, 0), b.…

A: Given function,  f(x, y) = (x + y + 2) 2 To find linearisation L(x, y) at i) (0, 0)  ii) (1, 2)

Q: Find the linearization z = = L(x, y) of the function z = f(x, y) = 3.x2 – y² + 5y at the point (xo,…

A: z=fx, y=3x2-y2+5y and the point is x0, y0=2, 1. Now, f2, 1=322-12+51=12-1+5=16 Now partially…

Q: Find the linearization of the function f (z) =23 at z = 1. L(z) = Using this linearlization, f…

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Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = x3y4 at a. (1, 1), b. (0, 0)

A: Consider the function: fx,y=x3y4 To calculate the derivatives of the given function with respect to…

Q: Let f(x, y) be a function such that F(s, t) = f(s – 2t, t²) fz(2, 1) = 5, fz(0, 1) = 3 fy(2, 1) =…

A: Explanation of the answer is as follows

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

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Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously f(x, y) = 1/x +…

A: Given:fx,y=1x+1y+xyfxx,y=0fyx,y=0

Q: Find ( fx fy, fzf xy f yx fxyz f zzx) for the function: f(x, y, z) = xyz + x²y + z³x + x²y?

A: To find the differentiation of the function

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = e2y-x at a. (0, 0), b. (1, 2)

A: Given:fx,y=e2y-x at   a.0,0    b.1,2Formula:Lx,y=fa,b+fxa,b.x-a+fya,b.x-b

Q: Q4: Find fz for f(x,y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1) %3D

A: Consider the function: fx,y,z=xcosy+3z+xyz. Find fz at 1,3,-1. Since fz=∂f∂z. Calculate partial…

Q: Find ( fx, fy, fz» fxy » f yx » f xyzf zzx) for the function: ух f(x, y, z) = xyz +x²y + z³x+ x²y²

A: Given:

Q: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

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Q: Find the linearization L(x,y) of the function at each point. f(xy) =x° + y° + 1 а. (4,4) b. (2,4)

A: Linearization: - We followed the tangent line to achieve a linearization of a function in…

Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: Find the divergence of F(x, y, z)= x î+y³ ₂² 7 +xz³ k. O1+3y²z²+3xz O1+3y²z²+3xz² 01+3y²₂² O 1

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Q: A. Find fxx, fyy,fyx, and fxy for the functions: 2. f(x, y) = In(xy) + tan(xy)

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Q: Find curl F if F(x,y,z) = 16y5₂5i - 8x³₂8 j- 7xy4k. O curl F = (-28xy3 +64x³₂7)i + (7y4 + 80y5z4)j +…

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Q: O Let f : A - B be an injection, and X, Y CA. Show that f(Xn Y) = f(X)nf(Y). |

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Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

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Q: Let f(r, y) = 2x² – 8y + 112. (a) Find and classify the critical points of f(r, y).

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Q4: Find f for f(x,y,z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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Q: Q8) Find the Linearization f(x.y.z) = x² + xy + yz +? at (1,1,2)

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Q: (b) If F = (5xy- 6x )i + (2y– 4x)j, Evaluate [F.dr along the curve C in the xy-plane, y =x' from the…

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Q: Find fxx, fxy, fyx, and fyy if f(x, y) = sin²(x – 3y) %3D

A: f(x,y) = sin2(x - 3y) fx = 2sin(x - 3y)cos(x - 3y) fy = 2.(-3).sin(x - 3y)cos(x - 3y) = -6sin(x -…

Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

A: Answer

Q: H.W: Find fr, fyy» fyx and fsy if f(x, y) = x+ y + xy XX ух

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Evaluate F.dr, where F(x,y)=[2y-3cos(x)]i + [4x +6sin(y)]j and C goes counterclockwise around the…

A: The objective is to evaluate ∫CF·dr where Fx,y=2y-3cosxi+4x+6sinyj and C goes counterclockwise…

Q: Let f(x, y) = xe Ty", find fr, fy, fræ, fay and fyy-

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Q: Find all functions f(x, y, z) such that grad f = 2xi + zj + yk.

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Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = 3x - 4y + 5 at a. (0, 0), b.…

A: fx, y=3x-4y+5 Partially differentiating with respect to x, we get fxx, y=31-0+0=3 Partially…

Q: Let T : R2 → R2 given by T(x, y) = (2x + y, x − 3y), (x, y) ∈ R2. Determine [T]αα , where α = {(1,…

A: We will find the images of (1,1) and (1,2) under the linear transformation T and then write them as…

Q: F(x,y)= (y² – 2x) i + 2xyj is conservative or not. If it is find a function f such that F = Vƒ.

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Q: Q.1 The natural domain of fur f(x,y) = lnx² + Iny is а) {(х, у):х > 0, у > 0}

A: Log function is defined for positive values

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

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

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Q: F(x,y) =(1+2xy²)î+ (2x³y +2y)j (i) Show that F is conservative and find f such that ỹf =F.

A: Given- F→x,y=1+2xy2i^+2x2y+2yj^ To Show- That F is conserative and find f such that ∇→f=F→.