b) Use Greens theorem to findf x² ydx – xy?dy where C is the circle x? + y? = 4 going counter clock wise.

Q: Evaluate the line itegral where C is the upper half of the circle z +y = 3.

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Q: 4. Compute, ydx + xdy x² + y² where C is the circle centered at the origin of radius 2 oriented…

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Q: Evaluate | dz where c is the circle z| = 2. z (z+4)

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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: Find the curvature k of the circle C : (x – 2)² + (y + 3)² - at the point (5, 1).

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Q: (c) Evaluate L A – 423 + 4z² dz where C is the circle |z – 2| = 1. , z4 – 4z3

A: Given,       ∮C4z+2z4-4z3+4z2dzwhere C is the circle z-2=1

Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

Q: Show that [(x- y) dx + (x – y)' dy] = 3ra" taken along the circle x +y =a° in C the counter…

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Q: Use Green'sTheorem to evaluate O ydx – xdy where C is the circle with center at the origin and…

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Q: cos TTZ 6. Evaluate -dz, where C is the circle |z| = 4 c 23-7z+6 ezt

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Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

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Q: 6) Find the area of the surface generated when the upper portion of the circle x + y? = 100 on the…

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Q: Find the center C(h,k) and radius (a) :of the circle x² + y° – 4x – 4 C(4, 3/2), a = 5 O С (4, 0), а…

A: Solution:-

Q: Evaluate (3y - esinz)da + (7x+ V +1)dy where C is the unit circle

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Q: Use Green's theorem to evaluate O -x²ydx + x°dy, where C is the circle x? + y? = 4 with a…

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Q: 글 36- +| de. 1 4 dz, (z+3i)³ ] Evaluate - z+3i where C is the circle |z+ 3i| = 6 + 4, 0 < 0 < 2ñ .

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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: Use Green's theorem to evaluate -y dx + x dy, where C is the unit circle r? + y? = 1

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Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

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Q: O Evaluate + z )ds where C is the circle F(E) = for 0EEE Zo

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Q: Please evaluate (3y – ein(e) dx + (7x + Vy* + 1) dy, where C is the circle a? + y = 9. Hint: use…

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Q: By Green's theorem, if C is the circle r + y = 4 taken anticlockwise, then z*dy, equals -27. none of…

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Q: b) Let C be the circle |z| = 4 traversed once in the positive sense e~2 (counter clockwise). Compute…

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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: Verify Green's theorem for $[xy² dx + x²y dy], where y is the circle x? + y² = 4.

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Q: zt e dz if t>0 and C is the circle z]=2. Evaluate 2ni C 2πίz+1

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Q: (y - eCos(e25! dx + (x2 + y+1) dy, where C is the circle r = 2.

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Q: Find the curvature k of the circle C:(x – 2)2 + (y +3) = 25 - at the point (5, 1).

A: circle equation is x-22+y+32=25 and point 5,1find curvature k

Q: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x-2)²+(y-3)² = 4 Without using Green's Theorem.

A: We will find out the required value.

Q: Compute . Z+1 dz, where C1 is a part of a circle with r = 3, and 0<0< %3D

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Q: Find the center and radius of circle x“ + y° - 2x-4y+1=0. Prove thot (0

A: I am solving question 1. if you want other question to be solved then repost.

Q: 6. In the accompanying diagram, PQ is tangent to circle O at Q and PRT is a secant. If mZP - 56 and…

A: To find : m arc QR

Q: 4. Let C be the the circle ² + y² = 4 and Calculate the work(W = [,F dr when C is traversed in the…

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

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Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

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 - – In(x² + y²))dx + 2 tan¬²(y/x) dy, C is the circle (x - 4)² + (y…

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Q: 6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented…

A: region of integration is part of circle, x2+y2=7, lying in 3rd quadrant, thus, limits of x,y are -7…

Q: In the following sketch, O is the centre of the circle. AE= ED and DT=TC. %3D Prove that (1) Ê =Ô¡…

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Q: Find the upper bound of |[∫c ez^2 + 1 / (z - 1)2 + 5] dz|, where C is the circle |z - 1| = 2.

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Q: dz b) C: z|= 4 is a circle calculate the integral .(z-1)(z² +9)

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Q: In R', the equation x² + y + z? = 4 describes a sphere of radius 2. Select one: True O False

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Q: Find the curvature K of the circle C: (x - 2) + (y+3)² = 16 %3D at the point (2, 1).

A: Given: Equation of circle C: (x-2)2+(y+3)2=16 ⇒ (x-2)2+(y-(-3))2=42 We know that circle equation is…

Q: (i) Evaluate $.z'dz, where C is the positively oriented circle |z- 1| = 1.

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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: 9. Determine the image of the circle z +- 2 P 1 2 3i under w(z) ==+l+i. Z

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: The DE for the family of circles of radius 9 is: A [1+ (y')²]³– 81=0 B [1+ (y')²]²- (» )²-[1+…

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Q: Let C be the circle |z| = 4 traversed once in the positive sense (counter %3D clockwise). Compute :…

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Q: $ ydx – xdy where C is the circle of radius 3 with center at (13, 28)

A: We use Green's theorem to evaluate the given line integral