) F(x,y,z) = 2x² – z² + 3xyz + y = 0 əz =? əz =? ду find I əz 4х+3yz əz Зxz+1 ' əy -2z+3xy -2z+3xy əz əz 4x+3yz Зxz+1 -2z+3xy kę əz əx -2z+3xy az 4x+3yz 3xz+1 ду əz -2z+3xy -2z+3xy əz 3xz+1 4x+3yz ду -2z+3xy -2z+3xy əz az 3xz+1 4x+3yz əx -2z+3xy ду -2z+3xy

Q: Find ∂y/∂x1 and ∂y/x2

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Q: y = Ce 2 + Cze-3r +7z Oy/" + - 6y+42-7 0 O y" +y - 6y+38r – 5 = 0 O y" +y - 6y+ 40r -9 = 0 O y" + -…

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Q: 3) A)-V2-a-2 3a.) (r)D 3b.) N(-2)-2 3c.) fxth)-f(x) 12-x+h) =D72-(x) (Jz-Cth)+

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Q: (x+y)^2=x^2 + 2xy + y2, subsitute (-2) for x,and (-1) for y, and check if the left hand side is…

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Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

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Q: Which of the following is the standard equation of 9y² – x² + 2x+ 54y+62

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Q: Let F(x, y, z) = x3³yz² - 6x²yz + 9xz - 2y³z. Find F Fxyz' 3x²yz² - 12xyz +9z+ x³z² − 6x²z − 6y²z +…

A: This question is based on Partial Derivative.

Q: 3 For V- , evaluate y' when y= 4. A) -4 B) 4 (c) -2 D) 2

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Q: Find the value of fa and fy at (1, -1) when 4 f(x,y) =+5x²+3y². xy 1. 1- = 9, f = = -7 2 2. f= = =…

A: use partial differentiation for finding the solution.

Q: (D² + 4)y = 0

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Q: a2u a2u 2y дхду a²u )Find du where ax - - axây' ay? u = x3 - 2x2 + 2y3 – 6xy + y ax2

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Q: 5. (x + 3): (5y - 2) = 1:4 and 2x + 3y = 4 6. x: y:z- 1:2:4 and x +y +z= 112 (x + y): (y - 2): 2 =…

A: solve the equations

Q: (3 da + dy = 0, y(-1) = 2. (y-2x) ry? %3D %3D 3.

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Q: Find the equation y = f(x) passing through the points (-11-21), (1,15), (2,12) and (3, 3)? Find also…

A: We will use the Lagrange interpolation method. We have: x x0=-1 x1=1 x2=2 x3=3 y y0=-21 y1=15…

Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: The derivative of flx)= - 3x -2x? is 5+ 4x

A: Given that -      fx=3x-2x25+4x     f'x=?

Q: Find y' for y = 8x³ + 5x² − 7x + 4 - A) 24x + 5 C) 83x² +52x - 7x B) 3x² + 2x - 11 D) 24x² + 10x - 7

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Q: If u = eª₁x+₂y+a, where a₁, a2, a3 are constants and 2² u J² u 2² u + = U. a² + a² + a² = 1. Show…

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Q: Let g(x, y) = 3.2³-6-2²-5.y2 +1. a. ag Show/hide

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Q: дz дz If z = f(x, y), find a and for the following equation əx ду z = x² + 3xy + y³

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Q: 5) The equations r² + y²s + yt² - 13 and y² + x²s + rt² = 9 define s and t as implicit Əs functions…

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Q: Find ∂w/∂v, if w = 3x4-5y3+z5-10, x = 3u-4v, y=5u+2v, z = u+8v. Write in terms of the two…

A: Chain rule of derivatives

Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: Find the derivative. 1) f(x)= V7,7x A) 7.7)4/5 B) 7.7)-1/56 ,7) D) 2) y = x/10x-8 15x-8 A) 15x B)…

A: 1) Obtain the derivative of f as shown below: f'x=ddxx7+7x5       =15x7+7x-45ddxx7+7x…

Q: 7x-4y-3z = 21 -4x+7y-z = 0 -3x-y+5z = 0 x, y, z?

A: Given

Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

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Q: If B = x°ya, + (2x + y)a, – (y – 2)a, find (a) V B (b) V X B (c) V (V B) (d) V x V X B

A: Given : B=x2yax +(2x2+y)ay - (y-z)az

Q: 3. Find the value of y when x = 0. a) y= 3x - 1 b) y= -0.5x + 2 c) y= 2x = 3(0) – 1 = -1 =-O.5LO)+a=…

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