Q1. Verify Euler's theorem for the homogeneous funetion, fxy.2)-axy +byz + czu

Q: A natural cubic spline S on (0,2] is defined by Jsin - 1+2-r. S) = if Osr<l. |S,0) = 2+ b - 1) + cư…

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Q: get an 6Usc Thesrmn to show that -x gra) = 2 has a unique haed %3D point on

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

Q: 6. Evaluate (7xi - zk) · ndA over the sphere S : x² + y² + z² = 4 (u) by the Divergence Theorem, (b)…

A: The divergence theorem states that  ∬SF·ndA=∭V∇·FdV Where, F is the vector field, V is the given…

Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det &gt;0 if both Eigen value positive:- The product of the…

Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: Let z be a complex mumber o B19) s and c be any then So BlE)dz+a fle) dz isequi contou any funckon…

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Q: Two functions u and v of x and y are said to satisfy the Cauchy- Riemann eguations if u, = v, and u,…

A: Thje given functions are,u(x,y)=y(x2+y2) , v(x,y)=x(x2+y2)

Q: 7. Use the Divergence Theorem step by step including sketch of the solid shape to find the flux f SF…

A: sketch of the solid shape is as follows

Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: Compute the Wronskian of the following equation. y" – 4y' + 4y = xe2x %3D

A: Given: y''-4y'+4y = xe2x

Q: Drag the postulate or theorem that proves the trieng AZWX AY XW a. ATSU AXVW # SSS E SAS

A: which criteria follow to congruent triangle

Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

Q: AXYZ is isosceles with base YZ and M is any point on YZ. Prove that a. ZXMY > ZY Z. b. XM < XY M

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

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Q: 8- Solve ihe separation of variable MeRod satisfy %3D The condilion as tp0 as for x=0 and a =a T=メ…

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Q: Exercise 2.8. Verify that q eAt-d satisfies the "martingale property" %3D u-d Sug + Sa(1 – q) =…

A: Given,  q= erΔt - du - d Consider ,  su q + sd (1-q) = su erΔt - du-d +sd1-erΔt - du - d= su erΔt -…

Q: 2. Let W be the union of the first and third quadrants in the xy- plane. That is, let W = xy 0 a. If…

A: According to our company gardening can answer only one question. If a specific questions are asked…

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

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Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

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Q: 3. Consider the ra greater across z =1-r² - y² plane and the s and a paramet

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Q: Considering f(, Y, z) = z + x²y and S as part of the cylinder y² + z² = 25 that is between the plans…

A: It is given that surface S is the part of the cylinder y2+z2=25 lies between the planes x = 0 and x…

Q: Find the bounded solution of au Əx = 2 อน at + U_if_U(x, 0) = 6e-³x. 1

A: Given: The equation is ∂u∂x=2∂u∂t+u and the given initial condition is ux,0=6e-3x. To find: The…

Q: 6. Determine the number of zero's for h(z) = 2z* – 3z² + 2z – 5 inside the disk |z| = 2. (Use…

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Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: Consider a dihedral groop Dy=<agb: asb= (abj=1 Ds cuss all Dy and verify Subgooups of "Dy=…

A: See answer below.

Q: 1. Compute SF · dr where F(x, y) = (y²,–x²) and C is the part of th parabola u = 12 from (-1 1) to…

A: First take dot product of f and dr Then put value of y in terms of x Integrate and raise limit of…

Q: Find the general equation f the plane passing through P(-!,3,-2) and having n(-2,1,-1) hormal. O so

A: The objective is to find the general equation of plane.

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: graup Consider a dibedral 2. Du= carb: d=b-(ab)"%=D1> Discuss all passible Commulators 'and verify…

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Q: t in 30 minute please duopoly with homogeneous goods. There ar

A: When there are only two firms in the industry, it is in their advantage to collude and set the price…

Q: A natural cubic spline S on [0,2] is defined by (So(x) = 1+ 2x – x³ S(x) = Is, (x) = a + b(x – 1) +…

A: Given: Natural cubic spline S on [0,2] is defined as: Sx=S0x=1+2x−x3 if 0≤x≤1S1x=a+bx−1+cx−12+dx−13…

Q: that ulx,y) = 42 Cos 3y is the particulas -3X prove Solution of Uxx+Uyy =0 u cx, 플) =0 where…

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Q: 1) Consider the solid Q in the first octant, generat surfaces: z = (y – 3)² + 1, 2r + 4z = 16, 1= 1,…

A: Volume of solid: Let z=f(x, y) and z=g(x, y) be the functions of x and y of a solid, and let x=a to…

Q: Find the bounded อน əx solution of อน 2 + U if U(x, 0) = 6e-3x. at

A: We have ∂u∂x=2∂u∂t+u  The initial condition is ux,0=6e-3x Now, ∂u∂x=2∂u∂t+u can be written as…

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

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Q: Show that the following system undergo a saddle-node bifurcation. Find the vale H= Ho where such a…

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Q: Calculate A and B so that t B %3D 1+1 (1-z²)

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Q: Sketch the solid described by the given inequalities. 0srs 8, -T/2 se S T/2, 0szs 1. 1.0 1.0 z05…

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Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D

A: Consider the given function. u=lnx2+y2 To verify the equation, find the derivative first with…

Q: • Verify that 3r is a one-parameter family of solutions of the DE ry + y = 3r. • Deduce a solution…

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Q: 6. A cable for a su sp en si on bridge has the sh ape of a parabol a with eqation y = kx². Let h…

A: Solve the above problem.

Q: 13. Point P is the centroid for AMNO. Calculate OQ if ON = 17. Round to the nearest tenth if…

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Q: 3.2. let f(x) = 2, x+4 xez, * 1 - 1 1/2/20 -74x45 -*>$ Approximate the foldoy using Trapezoid mule…

A: In order to approximate the integral: ∫abydx, the trapezoidal rule uses the formula:…

Q: Complex Analysis

A: For given function, First we will show the function is harmonic function as shown below :From the…

Q: Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented…

A: Given : a=2, c=8 We have to use Green's Theorem to evaluate            ∫C axy dy+cxy dy where C is a…

Q: 2 - Find the inter val on which f are Con Cave down and infleobion Points a -y = x2 5X+10 6- ソ= (¥+…

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Q: Evaluate / (7xi – zk) · ndA over the sphere S : x² + y² + z² = | S a) by divergence theorem, (b)…

A: a) By divergence theorem, ∬SA. ndA=∫∫∫V∇.A dV Now,  ∇.A=∂7x∂x+∂0∂y+∂-z∂z=7-1=6 By changing to…

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:…