Vx - Jy +1 lim (x ,y )→(4,3) x -y -1

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,…

Q: xY lim x,y)→(0,0) Vx2 + y? 2

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Q: Find ∇f(x, y, z) for the function f(x, y, z) = x2 + y2 − 4z and find the direction of maximum…

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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…

Q: 2. 2. Let そニと X=UV, y = sin v, Use ナ chain chain Rule to find Ev.

A: 1) The given function z=e2x2y+3xy2 Differentiate with respect to x taking y as constant…

Q: f(x,y)=x² +16xy + y² +8

A:

Q: Find the linearization at x = a. IT f(x) = sin³ (x), a = 4

A: Given,            The linearization at x=a.             fx=sin3x, a=π4We know that,             The…

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…

Q: Find each limit f(x, y) = 3x + xy − 2y

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Q: Find f-(x, y) and fy(x, y). f(z, y) = (y° tan(5z)) f-(x, y) fy(x, y) =

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Q: du -xy du Ifu =f(x² +2yz,y² +2zx) Prove that (y- zx)-(x² - yz) -NX ду

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Q: Vhich of the following is correct? A) dx = lim | 1 %3D xp- = lim 4 V.r+4 V.r+4 V.r+4 -2 V.x+4 B) S…

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: x – Y lim (x,y)→(0,0) Vx – Vy

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Q: 2t dt = 1 – t4 lim x→1- A) B) 2 C) 0. D) 1. 1

A: Given limx→1-∫0x2t1-t4 dt

Q: Use the limit definition of partial derivatives to find fx(x, y) and fy(x, y). f(x, y) = x2 − 4xy +…

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Q: y z lim (x,y,z)>(0,0,0) x² +4y² +9z .2

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

Q: Find the Linearization L(x) of y = (1+x)¬1/² at a = 8. L(x) = %3D

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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: Use the limit definition of partial derivatives to find f,(x, y) and f,(x, y). f(x, y) = x² – 8xy +…

A: We know, fx(x, y) = limh→0f(x+h, y) - f(x, y)h fy(x, y) = limh→0f(x, y+h) - f(x, y)h

Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Find domain and vange f (2y)- し、 (x'+ゴ) ) fCz, y) = Sin" (y-z) Ž (3,y)- tan

A: According to the question,  We need to specify the domain and range of the given function: (A) f(x,…

Q: Find the partial derivativef,for the functionf(x,y) - &x+y. 1,(x.y)- 17 1,(x.y) = Sx+y Sx ,(1.y) =…

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Q: Use the limit definition of partial derivatives to find f,(x, y) and f, fy(x, y). f(x, y) = x2 – 6xy…

A: Using partial derivative,

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: (c) lim v f(x) x→2

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Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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

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Q: Find the partial derivative. z = (2² + 2x – 6y)"

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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: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

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

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Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

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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: lim, - „f(x) = 0, then fx)dx diverges Select one: O True False

A: The given statement is

Q: Differentiate the function y = 6 + x using the Chain Rule. dy %3D

A: Given, the function is                              We have to differentiate this function using…

Q: Find the partial derivative. f(x,y)=x^3+5x^2y-8xy^3. Find fy(x,y)

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Q: XY lim メ)→(0,0)Jx2+ y2

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

Q: b) Use the chain rule for partial derivative to find 2 when z = f(x, y) = x²y + ln(x + y) and (x, y)…

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Q: lim (z,y)→(0,0) r* + 3y4

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

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Q: Use the limit definition of partial derivatives to find fx(x, y) and fy(x, y). f(x, y) = x2 − 5xy +…

A: We need to find partial derivative.

Q: Find f-(x, y) and fy(x, y). f(1, y) = (y^tan(4x)) fa(x, y) : fo(x, y)

A: The given function is: f(x,y)=y5 tan(4x)-43

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

A: