Verify that 1 1 9 = 2x²y + ²xy₁ - y² + 2y²-2² y ₁ u(x, y) = x²y +4² +2y²-2y + x²-3x - 29

Q: 2. If F = (3x² - 3yz)i + (3y²-3xz)-(32²-3xy find div curl

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Q: give the general formula of this amount b.) choose those polynomials that contain elements of the

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Q: if y = x+ v3+ 2x then prove that (3+2x2) + 2x 2y = 0 %3D dr

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Q: Ixe A) e¯(1 − x) + C el-r 1-x B) -I dx = +C x C) -e (x + 1) + C D) −æe¯ª + C E) e(x + 1) + C

A: Topic = Integration

Q: TEST FOR HOMOGENEITY: 2. x² - 5xy - 4y²

A: The given function is x2-5xy-4y2 We need to test the Homogeneity.

Q: Find an integer coefficient cubic that has x = 1 and x = 2+ /3 as zeros.

A: Given: The two zeros of a cubic polynomial are x=1 and x=2+3.

Q: 2 4 2) f(x,y)=2xy- 5x? - 2y² +4x+4y – 4 Ans. f 3'3 0 local max. %3D

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Q: 9) Solve: (x + y)dy-(z-y)dx=0 a) x² + y² = C b) z² + 2xy + y² = C c) z²-2ry+y²=C d) z²-2ry-y²=C

A: We need to solve D.E.

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

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Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

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Q: Find dy of 67 2. 2. my

A: The given equation is   yx=x2+2y2+1(ln y)x The product rule for derivatives is expressed as…

Q: Suppose z = x + iy and f(z) = z - 1. Find w = u + iv such that f(w) = 1 + 3i (A) 3+2i (B) 3-2i (C)…

A: We have given that , fz = z - 1 , where , z = x + iy Here , w = u + iv Let , fw = 1 + 3i We need to…

Q: EX:- Select Analog to Convert 2X + y - 3Z - 2u = 0 __(1) X + 2y +Z+ u = 0. (2)

A: We are given a linear system and we have to convert it into analog matrix form.

Q: Determine the values of x, y and z if (x+y+z)i + (y-z+1)j + (x-z)k=0. (x−y)i + (y+2z)j +…

A: A vector  is equal to the  vector if all the individual components are equal to

Q: x 6. Differentiate: y = x² + 3x - 1 A. C. x²+1 x²+3x-1 -x²+1 (x²+3x-1)² 0 2x²+3 eldet 10-(x²+1) B.…

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Q: Obtain characteristics y² Uxx + Uyy = O

A: Given equation is  y2Uxx+Uyy=0 Now comparing with  AUxx+BUxy+CUyy=0 We have A=y2, B=0, C=1

Q: + x(x*+ zy² + ig) dy= luy) dy 2. 2. 2) 3(x y) dx -

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2y4-6x3 +|1x=-37x-16 dx X3 - 3x2+5x-I5 2x

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Q: (х? + 2у — 10у3х) if z у? (у? + 4х + 5у) dz -, find || дх

A: Given:

Q: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 4- compute dw dw дх' ду at the point (-2,3) if w = (2x + 3y - 1) ²

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Q: Which of the following functions V(y₁, Y2) is a Lyapunov function for the dynamical system with…

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Q: x + 2y + 3z = 1 -3x – 2y – z = 2 Can be written as 4x + 4y + 4z = 3 3 -1 5 2 4 1 2 1 2 3 -1] | 1 0 1…

A: In given three equations, at first shift right hand side to left hand side then write it in form of…

Q: 2. x + y – z = 2   2x + 2y - 2z = ­6  5x + y – 3z = 8

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Q: 7. Integrate. So So (x-1)² x² + y2 dydx

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Q: Consider the two following graphs and answer the following questions. a) Are G and H isomorphic?…

A: The graphs given are as follows:

Q: Find curl (9z i + 10x j+ 6y k). curl(9z i+ 10x j + 6y k) = ( i )i + (i j +( )k

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Q: 4x = 0 %3D 4y + i = 0 x + y 8 = 0 (х, у, 1) %3

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Q: 10. Subtract 2- V- 64x²y* from – 3– xy-9y' and express the result in a + bi form

A: Answer and explanation is given below

Q: { 0 f) f(x) = 0≤x<3 3 < x < 4 Show Transcribed Text f(x + 4) = f(x) Find the Fourier series of the…

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Q: [x +1 0 2 1 2 (3)if A = 3 1 and B = 3 y -5 4 -1 -5 4 z - 4. Find x,у аnd z.

A: If two matrix A and B are equal then Each matrix of A and B has the same number of rows. Each matrix…

Q: Look for the annihilator of the given expressions. i) e2x sin3x ii) x³ e4x iii) 5x* - 2.x + 8x - 7…

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Q: Kindly exhibit that xzxx+yzxy=y2zyy if z=xy+yln(xy)

A: The given data is: z=xy+ylnxy To prove: xzxx+yzxy=y2zyy

Q: b) x²y + xy = 1 x>0 y(1) = 2

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