1). Let, 2=x+iy *,y€R. In this case, (a). Prove the equations 2-2+2 and a = i.2 %3D %3D

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), E (0,4,0), and (0,0,2)

A: The vertices of the tetrahedron are (0,0,0),(1,0,0),(0,4,0),(0,0,2).  x varies from x:0→1y varies…

Q: Solve the initial valwe problem using Laploce trensformotion. y (4) + 2y'(+) +5y(+) = esint y lo)-0…

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Q: If --kr, show that d? dr %3D dt

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Q: Solve the following first-order linear DE's. y' + (cotx)y = xcscx, y = 1

A: we have to find the general solution

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,2,0), and (0,0,4)

A: # Given integral is      ∫∫E∫ zdv

Q: 2) Show that the cosine(45°) = V2 * (0.707). Let “u" = 22.5°, use calculator. %3D - 2

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Q: det(A) Show that det(AB-') = %3D det(B)

A: Consider, Let A and B be the two n×n matrix, Now Consider, detAB-1 We know that the theorem, Let A…

Q: (b) Show by direct computation that D'Alembert's formula is a solution to the problem U-cUrx 0,…

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Q: Solve the following first-order linear DE's. y' + (cotx)y = xcscx, yE) = 1

A: Two ways it can be solved. 1)By making exact form 2)Using integrating factor

Q: (34) Compute SSp (6e3y + 1) dA where D is the solid triangle with vertices (0,0), (1,0), and (1,2).

A: Equation of the linejoining the points 0,0 and1,2  is  y-0x-0=2-01-0  Or,  yx=21=2  Or, y=2x…

Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: 1. If XM = 4, XN = 6, and NZ = 9, find XY. %3D %3D %3D 13 If XN 6, XM = 2, and XY = 10, find NZ. M.…

A: observe the figure

Q: mple. Compute AB and BA where 1 -1 A = %3D B = -2 2 3 4

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Q: find the Lineartransfromation T:Manz (R)R whose matrit Mp --

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Q: %3D Bi'

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Q: State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for…

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Q: To/t Integrate Ua ko To 3. Uz kg 2. eT-1

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Q: 18, where 1, 2, 5. Consider the solutions are there uation 2i Eg + Tg + Tar uovenba (a) if z1, r2,…

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Q: and 3 point Gauss Quadrature 2 By using e sfim afe : 2 dx メ-2 い)S, dx Nx

A: The given problem is to estimate the integral using 2 point gauss quadrature rule and 3 point gauss…

Q: show that fGx) = C,ex +C,e* s a solution to y for all real conatanto C, +C2, and then find C,, C,…

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Q: A natural cubic spline S on [0,2] is defined by |So(x) = 1 + 2x – x³, S(x) = if 0<x< 1, |Si(x) = 2 +…

A: Given Sx=S0x=1+2x-x3if 0≤x&lt;1S1x=2+bx-1+cx-12+dx-13if 1≤x≤2

Q: Solve the following first-order linear DE's. yE) = 1 y' + (cotx)y = xcscx, %3D

A: Proceed as shown below

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,2,0), and (0,0,4)

A: x varies from 0 to 1&amp; y varies from 0 to 2 and z varies from 0 to 4.

Q: 3. Show that S, has the presentation (x, ylx* = y? (xy) %3D %3D

A: Given: Group S4 We need to show that S4 has representationx,y|x4=y2=xy3=1

Q: In R', the point (1, 1, 1) does not belong to the cylinder x + y = 2. Select one: True O False

A: Given problem:- In R³, the point (1, 1, 1) does not belong to the cylinder x² + y² = 2.  True  False

Q: 4. A 5m x 5cm is cut from a corner of 20cm x 30cm. cardboard, find the centroid from the longest…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,3,0), and (0,0,2)

A: we have to find triple integral

Q: 7) If A = xz³i – 2x²yzj + 2yz*k, find VxA at the point (1,-1,1).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Consider the solid lih S,: X=4-y² そ=2

A: Surface: Surface, A two-dimensional collection of points (flat surface), a three-dimensional…

Q: of the b) nd y- Fons c) with point.

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Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: 1. Let s, =2+j8 md -, = 4+j36. Show that a. -1+- = -+- 1 -1- -2 -1 -2 = -1-2 -1 : b. C d. =2 ||

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Q: Compute, [(1 – ye-")dx +e¯*dy where C is any path from (0, 1) to (1, 2).

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Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

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Q: Find first and second fundamenta! Texm U-V e Cos 2sin U-V of

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Q: A natural cubic spline S on [0, 2] is given by So (x) = 1+2x- x³,0 sx<1 S(x) = s, (x) = 2+ b(x- 1)…

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Q: Determine the general solution for following Cauchy-Euler Equatio dy + 7x +5y = x³. i) dx2

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Q: Q1 : prove 1 2(1–z) 3(1--z) dydxdz = 1

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Q: 16. If ZSTU = (13r-6)', mSU = (21x + 8)', and mUT = 143', find mST. %3D %3D %3D T.

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Q: 1. Draw a sketch of the cylinder z= ==V36 – 4y2.

A: Given: z=1336-4y2

Q: Derive pz, 192. sjt9z, Hz(t), ez, čr: directly , if X ~ U (0, w) with r = 20, n = 30, w = 100. %3D

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: 6. Consider the following model: Yi = Bo+B,D11 + B2D21 +u; O if person i is a non-immigrant) where…

A: Dummy Variable Trap: It is defined as the scenario when the attributes are highly correlted. One…

Q: Solve the glven differentlal equation by using an appropriate substitution. The DE Is of the form Y…

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Q: ),22 %3D Problem I. Given z, = 3el(T76), z, = 2eiT/4), find: 1. Z1 + Z2 2. Z1 - Z2 3. Z,Z2

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Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: 11T |13T V2 - V6, determine the value of sec 60. Given that sec 12 %3D 12

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Q: (1,1) Evaluate [ (3x²+4xy+ix)´dz along y=x² (0,0)

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Q: 2 I| ysin(xy)dydx Н.W.

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Q: Suppose that the true model is () E+ and that it satishes MR1-MR6, but you estimate by OLS (II) W=…

A: From the given information, I yi=γxi+ei The OLS estimator of γ is, γ^=∑i=1Nxiyi∑i=1Nxi2 II…

Q: Find ¹JJ²₁ z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,2,0), and…

A: The solid E is the tetrahedron with vertices 0, 0, 0, 3, 0,0, 0, 2,0 and 0, 0, 1. Draw the solid E:…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.