EKample H (Z r) is Subring R de Sub ring (R,+

Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: find flux f Use divergence Be 1ector F-12z+2リズ分カーズド cut of Sphere *+jr* =9 theorem to 2 A ースK

A: given vector F→=12x i^+2yz j^-z2 k^ out of sphere x2+y2+z2=9 claim- use divergence theorem to find…

Q: Let f (2) = sin ł Z %3D (z-3)2 Find the residue of f(z) atz=3 %3D

A: Use the formula for residue.

Q: 7

A: We have to find out

Q: [Find div(F x G) and Curl (F x G) where F(x, y, z) = x²yi + y³z²j – 2z²k | and G(x, y, z) = 3xyi –…

A: Given Fx,y,z=x2yi+y3z2j-2z2kGx,y,z=3xyi-5yzj+4z2k

Q: Use Stokes's Theorem to evaluate ∫c F * dr (dot product) In this case, C is oriented…

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Q: Find div F and curl F if F(x, y, z) = x°i – 9j + yzk. - div F= curl F=

A: Divergence of a vector function F(x,y,z) is given by, div(F)=i∂∂x+j∂∂y+k∂∂zF and curl of vector…

Q: Find div F and curl F if F(x,y, z) = 4y®z³i – 7x°z*j – 3xy°k. div F=|0 curl F=

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Q: Using the Fundamental Theorem of calculus ( e'dt) is rcon(z) 1. -sin(x)ecos(x) – cos(x)exin(z) 2. –…

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Q: Find div F and curl F if F(x, y, z) = x°i – 6j + yzk. - div F= curl F=

A:

Q: %3D What is the principle part for f (z) = zez at its essential Singular

A: We have to find the principal part at the essential singularity of the given function ;      f(z) =…

Q: Prove that the Lagrange's fomula can be put in the form ø (x) f (x,) (x- x,) ø' (x,) P„(x) = £ %3D |…

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Q: The generalized product rule Use mathematical induction to prove that if y = uj uz U, is a finite…

A: If y=u1u2⋯un , then dydx=du1dxu2⋯un+u1du2dx⋯un+⋯+u1u2⋯un-1dundx

Q: If F(x, y, z)= xz i  + xyz j - y 2 k find curl F

A: given: F(x,y,z)=xzi+xyzj-y2k we have to find the curl F. as we know that if we have F→=Fxi+Fyj+Fzk…

Q: How do I prove this proof?

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Q: Prove that the Lagrange's fomula can be put in the form ø (x) f (x,) (x- x,) ø' (x,) n P„(x) = Ë r =…

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Q: Find curl(F x G) = V x (F x G). F(x, y, z) = i +5xj + 3yk G(x, y, z) = xi - yj + zk

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Q: 6. (a) State the Identity Principle for analytic functions on region N. (b) Prove that if f is…

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Q: Use Stokes's Theorem to evaluate F. dr. In this case, Cis oriented counterclockwise as viewed from…

A: given  F(x,y,z)=2yi+3zj+xk

Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

A:

Q: F(x, y, z) = e-* sin y i+ e-Y sin z j +e- sin x k

A:

Q: Find div F and curl F if F(x, y, z) = xz°i+ 5y*x²j +4z²yk. div F= curl F=

A: To find curl F and div F.

Q: 6) let F= é Cosy i + find a) Dirergne e siny į+ zk F 6) Curl F %3D F b)

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Q: tor field F = 21 + 4j + 3k across the surface S.

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Q: the region in w- plane which is image of the region 1 < z <2 in z- with the transformation f(z) =?…

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Q: (a) Plot R in both xy and uv planes. (b) Find the Jacobian of the transformation (c) Evaluate the…

A: u = x-y, v = x+y

Q: Divergence of radial fields Prove that for a real number p, with 3 — р |r|P (x, y, z) r = (x, y, z),…

A: We need to prove  where r=&lt;x,y,z&gt; and p is any real number.

Q: Find div F and curl F if F(x, y, z) = 15y^z*i – 11a°2°j – 5xy°k. - div F= curl F=

A: Here the given function is F(x, y, z)=15y4z4i^-11x6z6j^-5xy3k^ We have to find div F and curl F.

Q: Use Stokes's Theorem to evaluate ·[F. Use a computer algebra system to verify your results. C is…

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Q: Find div F and curl F if F(x, Y, z) = x°i – 4j + yzk. div F= curl F=

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Q: f:X-Y continuous map, kex a compact 70 If sef, then f(K) is compact

A:

Q: Using the definition of continuity directly prove that f : R → R defined by f(x) := x2 is continuous

A: Using the definition of continuity, the given question has been proved in step 2.

Q: Using the divergence theorem show that F.nds = 0, where F(x, y) = yi – x %3D and D is a unit disc.…

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Q: The Cauchy's formula for a Rectangle: Let Q be an open subset in C and f be a complex differentiable…

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Q: Ono. 6b) Proue Trut if f integrable [o,1, Hen on ei S znfcandx

A: Here f is integrable on [0,1] then we have to prove that limn→∞∫01xnfxdx=0

Q: Evaluate the integral |/ (curl F) •n dA directly for F= [2², -a², 0], S : the rectangle with…

A: In evaluation of surface integral, Stoke's theorem is very significant. It states the relationship…

Q: [Find div(F x G) and Curl (F x G) where F(x,y, z) = x²yi + y³z²j – 2z²k %3D and G(x, y, z) = 3xyi –…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y'x²j+ 2z²yk. div F= curl F=

A:

Q: Find div F and curl F if F(x, y, z) = x°i – 10j + yzk. div F= curl F=

A: To find the divergence and curl of the following vectorF→=x9i-10j+yzk

Q: Find div F and curl F if F(x, y, z) = 4º®Y¡ – cos yj+ sin² z k. - div F= curl F=

A:

Q: f:AxRxZ-> Rx R where. %3D is f injective ? is Prove it. f surjective?

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Q: 13. Verify if div(curl F) = 0 for F = (x - y) i+ (x + y)j+ zk. %3D

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Q: Verify the Green's Theorem for the fields F = 2ryi - 2.ry²j. Take the domain of the integration in…

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Q: Ol a fundtion f is nt defined at X =a Then it is not continuQus at z= q

A: Given,          A function f is not defined at x=a.

Q: Find curl F if F(x,y,z) = 7exy i-8 cosy j +5 sin²z k. curl F = -7xexy k curl F = -7xexy i curl F =…

A: In this question, we want to find the curl of given vector function.

Q: Find curl(curl F) = x (V x F). F(x, y, z) = 4x³yzi + yj + 4zk

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Q: Find div F and curl F if F(x, y, z) = xz*i+ 6y°x*j+4z²yk. %3D div F= curl F=

A: To find the divergence and curl.

Q: Find div F and curl F if F(x, y, z) = x¹i − 6j + yzk. - div F= 7x + y curl F zi X

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Q: 3. Use Cauchy's residue theorem to evaluate the function f(2) = z around (z– the circle |z = 2 in…

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Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution: