F(x, y) := x² + xy + y² – 1 y – x2

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: f(z) = (x²+y)+i(y²-x) is analytic

A: Let  fz=fx,yu+iv=x+iy the function must be continuous and differentiable at all points in it's…

Q: Find the linear approximation of the function f (x, y) = 2x – y+x?y - near the point (2,0). O 2x +…

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Q: Integrate f(x, y) = 4c®* - 0.5y using h = 0.5 with y(0) = 2 from x =0 to 0.5.

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Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: integrate ​f(x,y)=x2−y over the curve​ C: x2+y2=4 in the first quadrant from (0,2) to 2,2.

A: The solution are next step

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: Use the Chain Rule to find at aw w = x² + y² + z²; x = 10tsin s, y = 10tcos s, z = 9st² əs Find the…

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Q: find fy CX,Y) it (x,Y)=x2-8xy- 2y?

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Q: Find the linear approximation of the function f (x, y) y- 1 at (0,0) x + 1

A: We are given fx, y=y-1x+1. Here, we need to find linear approximation at (0, 0). Now, fx=∂∂…

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

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 fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: Consider the function f(x) = 2x³ + 71° – 8z2 – 8. Enter the antiderivative of f(x) + C

A: To find the antiderivative means integration of the given function

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: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

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Q: dz dz and of the function xsin(y+ z) – xy + z² = 2y. ду -. Find the əx

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Q: If Wly, Y2 Y3]= 0, then (y1, y2, y3) must linearly dependent, where y1, y2 , y3 are diffferentiable…

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Q: Find fr, fy and fz. f(x, y, z) = x – Vy² + z? |

A: Given f(x,y,z)=x-y2+z2. The objective is to find fx,fy and fz.

Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: Find the linear approximation of the function y = x at point xo = 1 .3 О а. у%3D Зх - 2 О Б. у3D 3х…

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Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

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

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

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Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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Q: What is the I.F of (x^2+y^2+1)dx+x(x-2y)dy=0

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

A:

Q: y = secx prove that d² y dx +y 2y

A: For y=sec x, we need to prove that d2ydx2+y=2y3. Here,            y''=secx''      =secxtanx'…

Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

A:

Q: y = x* + 1, y = 0, x = 1 around the ar axis.

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

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 the domain of f(x, y) = Vy+I y(1-x²)

A: Given: f(x,y)=y+1y1−x2 The domain of functions of two variables, f(x,y) are regions from two…

Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

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Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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Q: Find the gradient of f(x, y) = 3xty3 + 4x°y® at (1, 2).

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Q: Show that the function f(x, y) = x²y% + y° is homogeneous.

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Q: F(x) = F' (2) , where (t4 - 3t2 )dt %3D d. Vt dt x2 dx

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Q: а. max f (x, y) %3D 4x + 3ху + у S. t. х+4y— 29 3D 0 х+ 4у — 29 — 0

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Q: Determine the linearization of y = 4 – 2x at (1, 2). Then use it to approximate the value of y when…

A: It is given that, y=4-2x2  at 1,2 we have to determine the linearization of function. Then use it to…

Q: Let y = f(x1, x2, w), where x1 = 2w2 and x2 = w+1. Find dy/dw.

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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: f(z) = (x²+y)+i(y²-x) is analytic %3D

A: We have, fz=x2+y+iy2-x Compare the equation with fz=u+iv we will get u=x2+y and v=y2-x Now,…

Q: Integrate the function f (z) = (z - 8i)² from z = 0 to z = 4 + 4i along the line x = y.

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Q: Find df/dt using the chain rule and direct substitution. f(x,y) = squareroot(x2 + y2) , where y =…

A: Given f(x,y)=x2+y2   andy=t2  ,  x=t

Q: Find the orthogonal trajectories of x2 + y? – 2cy = 0

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Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

A: