1. (a) fo³ fo²² ƒ¯* (2x − y)dxdydz 7 2x (b)ff f(x) xe-dydadz (c) EydV, where E = {(x, y, z) | 0 ≤ x ≤ 2,0≤ y ≤ x, x − y ≤ z < x + y}

Q: Let f(x) = {ax² (2x + b differentiable (a) 1 at x = 1. x ≤ 1 x>1 (b)-1 . Find a so that f is (c) 2…

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Q: If (x, y)= x²y+e* , find; d. y е. b. $, с. Ф Q.4 (1)

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Q: (5) Consider the several variable function f(x, y, z) = xe²y + yeš + ze¬². Give a general formula…

A: The given function,   fx,y,z=xe2y+ye3z+ze-x

Q: Suppose y = f(x) satisfies dx 8x Vy + 1 for y > -1 and f(0) = 0 %3D . Find f(x). O f(x) = 4x4 + 4x?…

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Q: 1. Let F(x, y) = 25x³ + 120x²y + 192xy? + 102y³ – 300x – 450y. Find the following: | ƏF (i). OF…

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Q: 4x + y² R² → R²: f(x, y) = 2xy +1) If there exists a function F(x, y). such that VF(x, y) = f (x,…

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Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: If f(x, y) = x³y + ye2z then find fry ? None fry = 12x²y + 2e2 y° +2e2 2. 2.4

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Q: Find fry when 1. fxy 2. fxy 3. fxy 4. fxy f(x, y) = (x+2y)exy. = - (2 − xy)(x + 2y)exy (2 +…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: (b) -x X x + y y - 4y + 2z = - - (x, y, z) = 10 Z = 2 z = 1

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Q: (a) Prove the following relation: B(x + 1, y): B(x,y) x + y %3D

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Q: The function z(x, y) obeys, = -2e Which of the follow represents a valid first step for finding u(x,…

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Q: 16. Let f(x) be a differentiable function defined on [0, 2] such that f (x) = f (2 - x) for all x e…

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Q: Let f(x) = 5 – Vx² + 1 and g(x) = x -7. Then (f o g)( – 1) = %3D (fo g)(x) = || %3D

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Q: 7. (D5 – 2D³ – 2D² – 3D – 2)y = 0 8. (2D3 – D² + 36D – 18)y = 0; when x = 0, y = 0, y' = 2, y" = 4

A: Note:- this is multiple questions and you have not mentioned is here which question you want to…

Q: x²-y² x²+y2 (x, y) = (0,0) For which value of "a" the function f (x,y) is continuous? (x, y) = (0,0)

A: Continuity.

Q: Given f (x, y) = x2 – 6xy + 2y2, determine f (0, 0) f(-1, 2) f (5, 10)

A: Substitute the values for x and y in the function, f(x,y) to determine its value at (x,y) . Consider…

Q: 7 Find the fa, fy Of the following f(x, y). (1) f(x, y) = x ln(2x - y) fx (1), fy (2) = - (2) f(x,…

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Q: 12 f(x, y) = #(x² + xy), 0< x < 1, 0< y <1. + xy), 0 < x < 1, 0 < y < 1. 7

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Q: f(x +h.y)- f(x,y) For the function f(x.y) = 3x + 8y, find f(x +h.y)-f(x,y) %3D

A: Solution

Q: Let f(x, y) = x²y. Compute and simplify each of the following: (a) f(x + h, y) – f(x, y), and (b)…

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Q: x² + y² = (3x² + 2y² – x)², (cardioid) 0, y 0.5 -0.5 0.5 1 -0.5

A: Giv:    x2 + y2 = ( 3x2 + 2y2 x )2     Point: ( 0 , 1/2 )

Q: S(x) =- x-2 y 8(x)= Vx

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Q: Assume that f(z) = iz+2 then Re(f(2)) and Im (f(z))are %3D O a. y+2 Re(f(z))=- (v+2)° +x Im(f(z)) =…

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Q: dy then dx If y = In(x/x² + 1), 2x2 + 1 C) x/x² + 1 2a2 +1 D) x(x² + 1) x² + x +1 E) x(x² + 1) 1 A)…

A: Find the derivative

Q: Let's assume that f(x) = x² + c* x c=1 g(x, a) = a* x² + a*x Find a such that the following error is…

A: We have to find  such that the error  is minimum

Q: € N

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Q: If fx(x)= 1/(1+x²), and fy(y)= 1/(1+y"), X & Y are independent. Find fzw(z,w), if Z-6,5 XY and…

A: Given: fxx=11+x2 fy(y)=11+y2 Determine ∂(z,w)∂(x,y)…

Q: 1. (a) Find -and if f (x, y) = 3x? – y² – 5xy y (b) If f(x, y) = 4x?y+ xy² – 7xy then find + ду Je…

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Q: f/dy if f(x,y)

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Q: 4) Consider the function F(x) = f f (t) dt . Find F¹ (7). O F(7)-F(2) O f(x) O f(7) Of(7)-f(2)

A: Given query is to find indicated derivative.

Q: Q₂. if z=f(x+ct) + g(x-(t) then show that C²Z = Ztt XX

A: Given function: z=fx+ct+gx-ct We have to prove that, c2zxx=ztt. We know that, daxndx=anxn-1

Q: Let f(x) = x^2 − 2 and g(x) = x^3 − 2. a. Solve for any intersection of f and g. b. Draw the region…

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