i) Use the residue theorem to evaluate 2z+6 dz, where c is the circle |z – i| = 2. z²+4

Q: 6. For any closed surface S, prove that || CurlF.N dS=0.

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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: 1. What surface in R3 is represented by the following equatic x = 7

A: In this question we will use basic of geometry i.e concept of plane. We will draw the plane on the…

Q: 5. Let C be the circle x +y} =4_which is positively oriented. Let C, be the upper half-circle C1 =…

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Q: 10. Let C denote the positively oriented circle z| = 1. Show that - Ti 2sin(z) dz cos(z) dz 4 z(z²…

A: See the attachment.

Q: By Green's theorem, if C is the circle x2 + y? = 4 taken anticlockwise, then fv dz - z'dy, equals…

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Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: Let C be the curve of intersection of the parabolic cylinder x² = 2y, and the surface 3z = xy. Find…

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Q: 2. Let C₁ denote the positively oriented boundary of the square whose sides lie along the lines x =…

A: Given: Let us consider the given data, The lines x=±1y=±1 Circle,z=4 To show ∫C1fzdz=∫C2fzdz a) when…

Q: In the following sketch, EFG is a tangent to circle BFC at F. Prove that ABCD is a cyclic…

A: Given diagram is                                               EFG is tangent to the circle BFC.

Q: use green's theorem to evaluate ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4 counterclockwise

A: Given: ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4

Q: 3) Prove thet the xy-plane with constant curva tue k= urve In is o circle of radious

A: We have to prove that a curve in the xy plane with constant curvature k=1r is a circle of radius r

Q: 1) Evaluate F dr where F(r,y) = ri and C is the half of the circle %3D ²+y 3 16 lying below the…

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Q: Evaluate the integral eiz dz, (22 + 1)2 where C is the circle |2 + il = oriented anticlockwise.

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Q: Let C be the positively oriented circle x2 + y² = 1. Use Green's Theorem to evaluate the line…

A: Given: C is a positively oriented circle x2+y2=1.  Objective of the question is to calculate…

Q: Evaluate F dī , where F(x, y) = (e* +x² )î +(e' – xy²)ĵ and C is the circle x² + y2 = 25, oriented…

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Q: Prove that the circle {(x, y), x² + y² = 1} is hot homeomorphic to the interval [-1, 1].

A: We will prove this result by contradiction: Suppose there exists a homeomorphism between -1,1 and S…

Q: 16)- Consider the quadrature formula 6 | f(x)dx = Af (-6) + Bf(6) -6 If the degree of precession is…

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Q: Use Green's Theorem to evaluate the integral (2x? – y)dx + 4xdy where C is the circle x? + y² = 9…

A: To evaluate the given integral using green's Theorem.

Q: 3. a) Compute: f (Rez-3z) dz where I is a directed line segment from z = 0 to z = i. b) Let C be the…

A: To Evaluate:  (a) ∫Γ(Rez-3z)dz , where Γ: z=0 to i. (b) ∮Ce-zz2(z-5)dz, where C: |z|=4 oriented…

Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem states that "for closed curve C enclosed a region R then the line integral along the…

Q: where C is the circle |z = 3i| =4. 2.3 Use the Cauchy integral formulae to evaluate 22 1 (9 – 22)(2…

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Q: Please evaluate (3y – einl2) dr + (7x + V yt + 1) dy, where C is the circle x² + y² = 9. Hint: use…

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Q: Q5. Prove that the circle {(x, y), x² + y² = 1} is not homeomorphic to the interval [-1, 1].

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: A D E y 50 W V 20 70 В ZDCE= 90 AD = AE = AC = AB by the Hypotenuse Midpoint Theorem + Thus DECB is…

A: The given figure is- Given that AD=AE and AB=AC

Q: 3. Let C be the positively oriented circle |2| = 2. Compute the following integral: 726+글 exp(를)…

A: We have to find complex integral using Cauchy Gaurast Theorem. Cauchy-Goursat Theorem. If a function…

Q: Evaluate the line integral ſe ry²ds, where C is three quarters of the circle a² +y? = 1, oriented…

A: C is the three quarters of the circle x2+y2=1, oriented counterclockwise. The parametric equation of…

Q: 2. Use Green's Theorem to evaluate (7z +y) dy - (r² – 2y) dz where C is are the two circles as shown…

A: theorem:

Q: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

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Q: 17. Evaluate OF . • dr where C is the circle x +y² = 1, z = 0 and F=yi+zj +xk.

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Q: 23 +3 Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7. 22…

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Q: Verify Green's Theorem for: f4y³dx-2x²dy where C, oriented anti-clockwise, is composed of the…

A: To find the integral ∮C4y3dx-2x2dy where C is the positively oriented closed curve x2+y2=9, y≥0 and…

Q: 8. Let Ci denote the positively oriented boundary of the square whose sides lie along the lines x =…

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Q: The OT of the DE of the family of circles with center at the origin is x= ky B xy= k x-y= k D none…

A: Solution

Q: 1. [7.5] Using Cauchy Residue Theorem, evaluate 2z+ 22 + where the contour C is the circle |z – i| =…

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Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

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Q: Use Green's Theorem to evaluate §+(x² - y²)ẩx + xảy, where C is the circle x² + y² = 9. Select one:…

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Q: Use Green's Theorem to evaluate (1in z – 2y) dz + (x – ycos y) dy, where C is the circle (x – 4)² +…

A: Given: C is the circle x-42+y-42=9. ∮Cxsinx-2ydx+x-ycosydy. To find: Using Green's theorem, value…

Q: Q5. Prove that the circle {(x, y), z² + y² = 1} is not homeomorphic to the interval (–1, 1). 1

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Q: Given that o is the part of the surface z = 4 – x in

A: Given, the surface z = 4 - x in the first octant from y = 0  to  y = 2. If ψx, y, z=xyz, F(x, y, z)…

Q: Let C denote the positively oriented circle z-i=2. Evaluate the integral: 1 dz +4

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Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem

Q: Let F = -2yi + 2xj. Use the flux form of Green's Theorem to compute F·n ds where C is the positively…

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Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

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Q: Q5. Prove that the circle {(r, y), x² + y? = 1} is not homeomorphic to the interval [-1, 1].

A: Here we can prove this question using topological property connectedness.

Q: 5. Let C denote the positively oriented circle z- 1= 3. Evaluate the integral: 3 z +2z dz 3. (z- 2)

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Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x? +…

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