Is < ( x1, Y1, Z 1), (x2, Y 2, Z2 ) >= xjx + yjy+zźz3 an inner product on R'?

Q: Let C be the positively oriented square with vertices (0,0), (1,0), (1, 1), (0, 1). Use Green's…

A: Let's solve by using green theorem.

Q: Compute the double integral of (x – 2y) Væ + 2y o i over the quadrilateral with vertices (0, 0), (4,…

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Q: U V3-22- zt

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Q: Calculate the line integral f -y²dx + xdy where ŕ is the path y² = 2x − x² such that x>1 and y > 0.

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Q: Compute the scalar line integral x – yz ds where C is the line seg- ment from (0, 1, 1) to (1,0, 1).

A: Given  ∫C x-yz   ds    where C is line segment from (0,1,1) to ( 1,0,1)

Q: Prove that cosh-z = In (z + vz? - 1) %3D

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Q: use a computer algebra system to evaluate the triple iterated integral.

A: We have given a triple integral;

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0). (2,2) and…

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Q: Compute line integral of F(x,y) = (2x² – 3,₁²³)^² + (2x +34²) ↑ с over the following C F-dr SCF ¾ ç…

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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 symmetry to evaluate the double integral. 2xy J63 JR 1 + x ,10 dA, R = {(x, y) | -4 ≤ x ≤ 4,0 ≤…

A: Consider the given double integral, ∫∫R2xy1+x10dA, where R=x,y-4≤x≤4, 0≤y≤1. Consider the integrand,…

Q: Let u = (x²yz, ry z, ryz?). Compute curl i

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Q: Evaluate fz² In z dz using integration by parts 2 Onz-+ +c Oz-+ Onz-+c Oz² Inz - 2 + c

A: ∫z2lnzdz=∫(lnz)z2dz=(lnz)z33-∫1zz33dz+c=(lnz)z33-∫z23dz+c=(lnz)z33-13z33+c=(lnz)z33-z39+c=z33(lnz)-z…

Q: Find antideriuative Flx) of the an flx) = _8 sinx 13 + COSX functian such that FlO) = 1 %3D %3D

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Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: Show that y^3dx+3xy^2dy=0 is separable and exact

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Q: second going from (-1, 1) to (-2, 0). Compute the line integral -1dy – 1dæ.

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Q: Use Green's Theorem to evaluatc the integral x²ydx + xydy where C is the rectangle with vertices (0,…

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Q: Evaluate the integral: ∫ t2 sec2(9t3 + 1) dt

A: The given integral is, ∫t2 sec29t3+1 dt. Apply the u-substitution by taking u=t3. Then dudt=3t2.…

Q: Evaluate the iterated integral: dydx - 1/4 Jx2

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Q: Use the transformation u = - -6x +y, to evaluate the integral [ ( (5x • y) dx dy, where R is the…

A: use the transform u=-6x+y, v=5x+ywe evaluate ∫∫R 5x+y dx dywhere R is the parallelogram bounded by…

Q: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

Q: Describe the bifurcation for the following dy - Ay - y %3D dt

A: The saddle node-bifurcation: Let y˙=f(α,t) is the system of equation, the to find the saddle-node…

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: Use the transformation u = y - x, v = y, to evaluate the integrals on the parallelogram R which has…

A: We need to evaluate the integral: ∬Ry-xdA using the transformations: u=y-x, v=y. Here, R is a…

Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: What is the integrable form of et dr? ex – e -x [(1-u²) ² du O Swi-) - 1) 2 du (1- " (D 2 du

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Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

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Q: compute J secx dr. I n trying to integrate

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Q: Solve by Laplace transform Utt - 9urz = 0, 0 0 u(0, t) = u(T, t) = 0, %3D u, (x,0) = 0, u(x,0) = 2…

A: Use Laplace.

Q: What is the largest possible magnitude of Curl(F) where F(x, y, z) = (4, a/9 – y?, 6z)? у, х

A: Given that F→x,y,z=4,x9-y2,6z

Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

Q: Evaluate the double integral I2 = || y'dzdy T where T is a triangle with vertices (-4, 0), (0, 1),…

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Q: Use symmetry to evaluate the double integral. x' dA, R = [-4, 4] × [0, 5]

A: Replace dA by dxdy x is from -4 to 4 y is from 0 to 5

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: Evaluate the improper intergal dx using the residue 2 (x² + 4)² theorem.

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Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: Explain Bessel equation and Prove that 2 (i) (ii) In+3X + Jn+5X =÷(n+ 4)Jn+4x 4J"n = Jn-2 – 2Jn +…

A: Definition Bessel's Equation: The differential equation x2d2ydx2+xdydx+x2-n2y=0 where n is a…

Q: Let i = (x²yz, ry z, zyz?). Compute curl i

A: The given vector is: u→=x2yz, xy2z, xyz2

Q: #1. Evaluate (2x – 5y) dA, R where R is the parallelogram with vertices (0,0), (2,3), (–1,4) and…

A: The given region R is a parallelogram with vertices as shown in below graph. We have to use change…

Q: (Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented…

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Q: Evaluate the iterated double integral. I 3 3y be dady A

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Q: Evaluate the integral dz dy dr. -2 Jo 5-722-7y2 32

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Q: (B) Compute div F and curl F for F= x²yi- (z3-3x)j + 4y2k %3D

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