Evaluate f. F• dr by using Stoke's Theorem, where F = zi + xj + yk and C is perimeter of closed triangle of the plane x+ 2y + z = Q in the first octant in the (b) counterclockwise direction, when viewed from the positive z-axis.

Q: Consider the function f(x, X2, X3, X4) = x+3XX4+2x2 8xxX4 +3x+7xa? O a. Fis positive definite Ob.…

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Q: Consider the right triangle withvertices (0, 0), (0, b), and (a, 0), where a > 0 and b > 0.…

A: Given right angle triangle has vertices  (0, 0), (0, b), and (a, 0), where a > 0 and b > 0.…

Q: b) Use Gauss' theorem to evaluate ff F - ndS where F = (r - y)i + y²j+ (ry-y)k and o is the closed…

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Q: The domain of the functi f (x, y, z) = In(3.xy – 6) {(x, y, z) e R³ : xy 20 {(x, y) € R² : xy 2

A: Consider the function  f(x,y,z)=ln(3xy-6)

Q: 3. Evaluate [[[ 20 av G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Solution :

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Q: Use the Cauchy-Riemann PDEs to determine all points z = x + iy ∈ C in which the following functions…

A: First separate real and imaginary components. Then apply C-R equation.

Q: Find c > 0 c > 0 such that the area of the region enclosed by the parabolas y = x 2 − c 2 y = x 2 -…

A: To find the value of c given area between the curves.

Q: 2. Evaluate F.ndS for the given F and o. (a F(x, y, z) = xi+ yj+zk, o: the surface of the sphere x²…

A: Given: F→=x i^+y j^+z k^ σ: the surface of sphere x2+y2+z2=4 Evaluate: ∬σF→.n^ dS Using Gauss…

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A: Find the maximum of the function fx,y=x2+xy+y2 on the unit circle x2+y2=1 using the method of…

Q: Determine the area that lies under f (x,y) = 9x² + 4xy + 4 and above the rectangle given by [-1,1] ×…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Use the divergence theorem to evaluate ]] F .dɔ̃ where F = xyi – ¹⁄y²j+zk and the surface consists…

A: Here, the surface consists of the three surface z=4-3x2-3y2; 1≤z≤4 on the top x2+y2=1, 0≤z≤1 and z=0…

Q: fj+1 - fj-1 2Ax Assuming a uniform grid spacing of Ax, derive a finite difference approximation to…

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Q: Let G be the solid enclosed by the plane z= y, the xy-plane, and the parabolic cylinder y = 1-x². If…

A: Consider the given information,

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y = x² – c² and y =…

A: Given information:- Find the value(s) of c such that the area of the region bounded by the parabolae…

Q: Use Lagrange's multiplier(s) to find the maximum and minimum for f(x, y, z) = x² + 2x + 2y2 + 3z2 on…

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Q: (1) Verify that the real-valued function u(x, y) = xª – 6æ?y? + y* + 4x – 6y + 2 - defined on the…

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Q: Use the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique solution in…

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Q: 4. Evaluate fo F• dr by the Stoke's theorem, where F = -y? î+x j+ z² k, and C' is the curve of…

A: Given :

Q: & 10 Let 20xx,y)=x² be a function defined by on al disk I in the positive quadrant containing the…

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Q: If F = 3zi + 4xj + 2yk and the boundary of the portion of the paraboloid for which z 2 0. C is the…

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Q: Use Stoke's theorem to evaluate F dr where F(x,y, z)=e-7i+ +e"k and C is the boundary of the part of…

A: Let Fx,y,z be a vector field and the surface S is bounded by a simple closed curve C. The Stoke's…

Q: Prove that | f(2)dz → ViRes(f, zo) 8 → 0. by letting Is = {z = 20 + de®; 0<0<¥} %3D where f is…

A: Given: Γδ=z=z0+δeiθ; 0≤θ≤Ψ where f is analytic in a neighbourhood Bz0, r except for a simple pole at…

Q: Show that the functions o,(x) = sin(nax²), for n = 1,2,3,..., form are orthogonal set with respect…

A: Consider the equation

Q: Suppose f(z) = z+z-2i 15 Define f(i) in such a way that the new function is . z +i continuous of…

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Q: 7. Use the Divergence Theorem to evaluate ff(F n) dS, where S is the top half of the sphere r+y + z…

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Q: a) Evaluate f, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

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Q: Evaluate F.ndS for the given F and o. (b) F(x, y, z) = (x² + y) i+ xyj– (2xz + y) k, o: the surface…

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Q: Find the area of a region enclosed by the parabolas f(x) 2 > 12 - 1 for all z in [0, 1]. = T and…

A: Topic = Area

Q: Q8) The planes 3x+6z=1 and .2x+2y-z=3 are orthogonal F O

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Q: Use the Cauchy-Riemann PDES to determine all points z =z+ iy € C in which the following functions…

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

Q: Consider f, g E T° (R") and 0 > 0. Show the following results on the subdifferential. (a) a(0f)(x) =…

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Q: Find the residues of f(z) = z²-2z (z+1)²(z²+4) at all its poles in the finite plane.

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Q: to find the use lagrange Multiplier Point p (x1s,Z) Closest to the origion on the Plane 2x +y - 2=5…

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Q: Please solve

A: Consider the given function.

Q: Given F=. By using Gauss's theorem, find f F ds for a paraboloid x = 4-y² - 2² with x ≥ 0 as shown…

A: We are given  F=-3x+1+z3,y+1+x3,6z+xy So, the divergence of F is div…

Q: 5)Evaluate F - nds for F = y²zi + y°j+ xzk using Gauss' Theorem. Consider that S is the boundary of…

A: We will find out the required value.

Q: The space is CJ0,2r] and the inner product is (f.g) = J r9gt) dt. Show that sin mt and sin nt are…

A: Given m≠n∫02πsinmtsinntdt=12∫02πcosm-nt-cosm+ntdt=12sin(m-n)tm-n-sin(m+n)tm+n02π=0

Q: 8. Evaluate F. dr using Stoke's theorem when F = (2xy — x²)ī — x² − y² )ī and C is the boundary of…

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Q: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

Q: use Stoles's Theorem to evaluate F ds where Ě= and C is the orde with rading 5 centered C2,0,0…

A: According to Stokes' law:                                                     ∮JF·dr=∬S(Curl F·N)dS…

Q: Let C be a closed contour and zo be inside C. If P(z) is a polynomial of degree n, prove that P(z)…

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Q: Y A B C Given: XC bisect YB at A; A is the midpoint of YB Prove: AXYA = ACBA

A: We have to prove that given Triangle are congurent.

Q: Use the Cauchy-Riemann PDES to determine all points 2 =r+ iy €C in which the following functions are…

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1. If…

Q: . For n, m 20 and n # m, show S' T.(z)Tm(7). VI- -dr 0 This is called the orthogonality relation for…

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Q: Verify Green's Theorem in the plane for F = (x² + y²)î + (x² – y²)f in the anti-clockwise direction…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.