(1 point) Let C be the positively oriented circle z2 + y-1. Use Green's Theorem to evaluate the line integral e i5ydz + iOzdy

Q: Let C be the curve which starts at the point (1,1), then moves in an anticlockwise direction along…

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Q: Does the Divergence Theorem apply to surfaces that are not closed?

A: By Stokes' theorem:

Q: Let C be a circle lying in the plane x+ z = 2 with center at (1,0, 1). Evaluate the line integr V2…

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Q: Calculate 8-z -dz, z(4-z) where C is the circle of radius 7, centre 0, negatively oriented.

A: C : circle with radius 7 and centre 0, negatively oriented  f(z) = (8-z)/(z(4-z)) Singularity of…

Q: Calculate the line integral ∫Cy2ds, where C is a part of the circle x=acost, y=asint, 0≤t≤π/2.

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Q: Let C denote the circle of radius 1 in R2 centered at the origin, oriented counterclockwise. for…

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Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

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: Sketch the surface z = f(x,y). f(x, y) = -x 2 - y 2 USE GEOGEBRA

A: Function f(x, y) = -x2-y2 To Sketch the surface z=f(x, y).

Q: Verify Green's Theorem where F1=y^2-7y , F2=2xy+2x and the curve C is a circle x^2+y^2=1

A: Given: F1=y2-7y , F2=2xy+2x and C is a circle i.e., x2+y2=1 As, we have:…

Q: State Green's Theorem. Use it to calculate . ((13x – 5y)i + (13x + 5y)j) dr where C is the circular…

A: We will find out the required solution.

Q: 2.2 Find upper bound of z + 4 -dz (z – 3i)3 + 1 where C is the circle |z – 3i| = 4.

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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: The value of the line integral I- [Adl where A-(2x+y)£+(y-x)ý along the parabola y=x^2 and form…

A: Evaluate: I=∫A.dl              ...(1)WhereA=2x+yx∧+y-xy∧

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: Let C be the circle |2- i 2 oriented counterclockwise. Evaluate the following integral 1. z(2² + 4)

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Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

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Q: 82. Use Theorem 6.10 to prove that a sphere of radius 5 has surface area 1007.

A: Given ,radius of sphere=5 We know, surface area (S) of a sphere of radius r units is given by:…

Q: Exercise 5. Show that there exists at most one closed geodesic on a cylinder with negative…

A: We will assume S ⊂ R be a surface homeomorphic to a cylinder and with Gaussian curvature K < 0.…

Q: Find a parametric description for the circle x2+y2-6y=0, oriented clockwise and where t begins at 0.…

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Q: (1 point) Let F = -3yi+ 2rj. Use the tangential vector form of Green's Theorem to compute the…

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Q: Are |z], Img(z) analytic? Give reason. sin Choose the suitable theorem to find the result of $ dz…

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Q: Find parametric equations for the circle x2 + y2 = a2, using as parameter the arc length s measured…

A: The given equation of circle is,

Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = <u,v,uv> , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: Sketch the surface 2./4- and verify that fry - lyx

A: Given surface is  z=4-x2-y2 we have to sketch this and verify that fxy=fyx

Q: Integrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. dz z² + 16z +…

A: Use Cauchy Residue theorem to evaluate this integral.

Q: Suppose a point X lies in the exterior of a disk, and suppose that two lines are drawn from X…

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Q: 11. Circle in the plane z = 1 with center (3, 2) and passing through the origin.

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Q: Use Green's theorem to evaluate $ 2y3 dx – x3y² dy, where C is the positively oriented circle of…

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

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Q: Let F (tan-(3x) + y)i + (2x + sec-ly)j and C be the boundaries of the %3D circle x? + (y- 4)2 = 9 in…

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Q: Find the length of the circle of radius r defined parametrically by x=rcost, y=rsint,0≤t≤2π.

A: Here I am attaching image so that you understand each and every step.

Q: Let C consist of the part of the circle r +y = 4 from (2,0) to (0,2), Followed by the line segments…

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Q: By using Cauchy's integral formulas evaluate sin Tz2 + cos TZ² dz (z + 1)(z – 2) C and e2z dz (z –…

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Q: 4. Let C be the positively oriented circle centered at the origin with radius r> 3. Without…

A: Given: Let C be a positive oriented circle centered at the origin with radius r>3. Without…

Q: Draw the parameterized surface. (Decide on a reasonable domain for u and v.)

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Q: Let Ci be the line segment from the origin to (3, 2,0); C2 be the shorter circular arc of the circle…

A: The three curves given are as follows: C1: The line segment from 0,0,0 to 3,2,0. C2: The circular…

Q: Find the centroid of the arc of the circle r = 2sin0 + 4cos0 from 0 = 0 to 0 = T1/ %3D O (2.637,…

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Q: Calculate 8 - z 'zp- z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented.

A: In this question we have to find the Integration.

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 3 : (3t, r = be a curve in 3-dimensional space having unit tangent and normal vectors u and .…

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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: 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: Let YR be the circle of radius R with counter clockwise orientation. Prove that 1 -dz = 0. lim z3 +…

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Q: Determine all singular points of the projective plane curve C whose affine equation is given by (y…

A: Consider the function fx, y=y-x22-y4. Observe that, ∂f∂x=0∂∂xy-x22-y4=02y-x2 -2x=0x=0  or   y=x2

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

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