6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented positively) and G(x, y) = (3x², 4y°).

Q: 22 Calculate 8 - z dz, where C is the circle of radius 7, centre 0, negatively oriented.

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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: e? – 1 (b) ( - 1y2 dz where C is the positively oriented circle |2| = 3. %3D z(z – 1)2

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Q: Q2 Calculate 8- z dz, z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented.

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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: T. 9. TO = PO 10.Sector of a circle is the region bounded by two radii and their intercepted arc.

A: here we check whether the given statement is true or false.

Q: 2. Evaluateſ. a+ (z+30:) dz along C which is the circle |z + 3i| = 3, counterclockwise. %3D (z+3i)

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Q: B) Evaluate S Ln z dz around the circle | z| = 2 %3D

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Q: 4 and Consider the region in the second and third quadrants between the circles x² + y² = x² + y² =…

A: Concept: cartesian coordinates can be converted into polar coordinates using trigonometric functions…

Q: 4. Let C denote the circle |z – 2i| = 1, taken in the usual counterclockwise orientation. Compute by…

A: Given: Let C  denote the circle z-2i=1 z-2i=1x+iy-2i=1x+iy-2=1 So, Centre of circle will be 0,2 and…

Q: 6. Evaluate [(x + y²)dx – xdy where C is the circle "x²+y² : = 1" with a counter- clockwise…

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Q: Q2 Calculate 8-z dz, z(4-z) where C is the circle of radius 7, centre 0, negatively oriented.

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

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Q: Let S(x, y) = x² +y² – 2x – 16y + 10 = 0 be a circle and L(x,y) = x – 5y + 10 = 0 be a line. 1. Find…

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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: 2: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x–2)²+(y-3)² = 4 | a) Using Green's Theorem

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Q: 6. Let C C R? be the positively-oriented boundary of the graph of the circle x2 + y? = 1. Using…

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Q: =2) Calculate & ydx + xz² dy - zy³ dz, where c is the circle x² + y² = 4, Z=3 (conterclockwise)…

A: We will use stokes theorem to find integral

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

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Q: 2. Find the DE of all circles with center on thex - axis.

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Q: Find the DE of a family of circles with center at (1,-2). Hint: Equation of circle with center (h,…

A: We know that equation of circle with center h, k and radius r is given by, x-h2 + y-k2 = r2 We have…

Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x2 +…

A: According to the given information it is required to calculate both sides of the Green’s theorem.…

Q: 6. Prove (by plot) the equation (x²+y²=16) is the circle in 2D , and cylindrical in 3D.

A: We will answer the first question since we don't answer multiple questions at a time. Please…

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

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

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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: 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: 4. Evaluate / (z – 2) dz where C is the lower half of the circle |2 – 2| = 4.

A: Note: According to bartleby guidelines we have to answer only first question please upload the…

Q: Exercise 1.2.16 Find the circle x2 +y² +ax+by+c=0 passing through the following points.

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Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense cos 3z (counter clockwise).…

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Q: (27=2 + 26xy + 10x – 2y°, 13x2 + 30y² + 2x³ + 22y)and let C be the circle a2 Let F = + y = 4…

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Q: 5. Evaluate (y +tan x)dx+(x -2ry+y)dy, where C is the circler +y' =4 and is oriented in a positive…

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Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: 2. Find the area of the smaller loop of the curve r = = 3( 1- 2cose)

A: We will solve the following

Q: z+i dz , where T is the circle Iz – 3i| = 1 traversed once (2) Compute counterclockwise.

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

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

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Q: What is the equation of the circle concentric with circle(x-2)2 + (y+1)2 = 5 that is tangent to the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: Given that region between the circles x2+y2=4 and x2+y2=25 and below the line y=-x and the region is…

Q: Q2 Calculate 8- Z -dz, (4 – 2) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(ry)j, F = Vf(x,y), and C is the segment of the parabola y =…

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

A: Cauchy integral formulae: Let f(z) be analytic in a region D, derivatives of all orders are also…

Q: 8. centered at Which of the following equations represents the circle with radius F 16x2 + 16y2- 16x…

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Q: Find the exact length of the curve. y = In(1 - x²), o sxs

A: Find dy/dx, then put it in the arc length formula.