x-y+7Vx - 7Vy lim Vx - Vy (x,y)→(0,0) x+y

Q: x' = -x 22. Find homeomorphism H for {y = y +x³ near origin.

A: Given that  x'=-xy'=y+x3 The solution for x'=-x is x=Ae-t The solution for y'=y+e-3t is,…

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Q: (a) Find the solution of the limit using polar coordinate system. x² + y² x2 + y2 lim(x.y)-(0,0)

A: To find the solution of the limit using polar coordinate system lim(x,y)→(0,0)x2+y2x2+y2 We have the…

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Q: (b) lim (z.y)→(0,0) Vr4 + y3 +1–1

A: limit of the rational function

Q: z + 14z + 49 f(z) = f(7) =| lim f(z) = 1. %3D z2 - 14z + 49

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

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A: Given limit, limx,y,z→0,0,0yzx2+4y2+9z2

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Q: limx→o (t+1)f(t)dt Assume f (0) = 4 %3D 3x2

A: Explanation of the answer is as follows

Q: A) F(x, y) = (x sin(x² + y²), ysin(x² + y²)) xy B) F(x, y) = x/y² + 1 y² + 1 C) F(x, y) = (yecos(=),…

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Q: of For the function below, use the limit definition of partial derivative to compute and at ôx…

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Q: e2x tan xy = lim (x.y)-) %3D (A) Does not exist (B) e2 (C) 0 (D) e2 (E) e

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Q: Y : k=0 y' + (2x + 1)y = 0, rrence relation. For k > 0,

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Q: f(x, у) 3D 5x2 + 9у2 f(x + Дх, у) — f(x, y) (а) lim Ax → 0 Ax f(x, у + Ду) — f(x, у) Ду (Б) lim Ay →…

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Q: 5x - 5y2 lim (z.y) (0,0) 7z+7y () Limit DNE 0. O 5/7 O 5/7

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Q: Identify the removable discontinuity. x² – 1 f(x) : X- 1 (х, у) %3D Additional Materials

A: A removable discontinuity is one at which the limit of the function exists but does not equal the…

Q: Find the partial derivative. 2) Let z = f(x.y) = 8x2 - 12xy + 4y3. Find z ax A) 16x + 12y2 C) 16x -…

A: As per our guidelines we are suppose to solve only one question if the multiple questions are…

Q: xy + yz + xZ lim (x,y,z)→(0,0,0) x² + y2 + z²

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Q: Use the limit definition of partial derivatives to compute the partial derivative of the function…

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Q: Example. Find extremals of functionality: under the boundary conditions y (0)= 4, y (2) = 6;

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Q: a) f(x,y) =3y%-2y8-8x²-bxy find the caftical potnts of thi's function.and determine points quality.

A: Hello, thanks for your question but according to our policy I am answering the very first question.…

Q: dy + 2xy = f(x), y(0) = 6, where dx f(x) = lo, x, 0sx< 1 x 2 1 0 sx < 1 y = x 2 1 Use a graphing…

A: Linear differential equation of first order : The most general form of a linear differential…

Q: XY lim メ)→(0,0)Jx2+ y2

A: Calculate the limit using polar coordinates as following:-

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Q: 1. Evaluate lim 2. Find the Ist order partial derivative of R(x.y) = Find dy/dx if x = e2t and 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: Find both first partial derivatives. h(x, y) = e-(x° + y9) h,(x, y) = %3D h,(x, y) = %3|

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Q: se the limit definition of partial derivatives to find ôz/ôx and dz/ðy. = x - 7xy + y

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Q: ecos a tan(z+ x) 2x – y+ z V4x2 + y – z xyz T T T x + 2y + 3z 3x + 4y – 2z, x + y + z

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Q: maximize f(x,y)=xy subject to the contraint 6x+y=18  the last question is what is the maximum valye…

A: max . fx,y=xyS.t 6x+y = 18     6x+y=18⇒ 6x+y-18=0∴ gx,y=6x+y-18=0    Fx,y,L=fx,y-L g x,y⇒…

Q: e2x tan xy = lim (x.y)- (A) Does not exist (B) e2 (C) 0 (D) e2 (E) e

A: We have to find the limit .

Q: Vx - Jy +1 lim (x ,y )→(4,3) x -y -1

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Xy + yz + z lim (x,y,z)→(0,0,0) x² + y² + z²

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Q: Find fzyx If f (x, y, z) = ln(x2 + z) + y2exz

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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: Use the limit definition of partial derivatives to find f (x, y) and f (x, y). f(x, y) = x2 - 2xy +…

A: Given query is to find the partial derivative.

Q: If y(x) is a solution of y' = (y+1)(50 – y) with y(0) = 0, what is the limit of y(x) as x approaches…

A: Given: yx is a solution of y'=y+150-y. Also, y0=0. To find the limit of yx as x→+∞. As, y'=y+150-y.…

Q: find absolute maximum and minimum of f(x,y)=x^3+3xy-3y^2+2 in a region whose vertices at (-1,-1)…

A: Given function is  fx,y=x3+3xy-3y2+2

Q: Find both first partial derivatives. h(x, y) = e-(x* + y4) h,(x, y) = h,(x, y) =

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