c) By using Green's theorem evaluate $ (Ary – y*) de + (* + 3ry) dy where C is a closed curve starting from the origin to point (0, 1) along the y-axis, then to point along the semi-circle x = -V1 - y?, then on a straight line, back to the origir

Q: c) By using Green's theorem evaluate $ (4.cy – y*) dx + (2³ + 3xy) dy where C is a closed curve…

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Q: Let C be the closed curve indicated in the diagram. Use Green's Theorem (2,1) (o,i) (x² + y?, y³ +…

A:

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

A:

Q: 4) a) y»*>O impenting y= # Curve, x =0 and y Colculote the orea af the regien betueen the lines by…

A: Solution to section (b) as requested:

Q: Find a formula for the distance from the point P(x, y, z) to the yz-plane.

A:

Q: Verify that Green's Theorem is true for S,3(y? – x) dx + (x2 - y)dy given that the curve C is formed…

A: We have to solve the given integral by Green's theorem.…

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

A:

Q: Use Green's Theorem to evaluate pxcosydx – ysinxdy, where the curve C is the square with 0), (TT,…

A:

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: 3.use Greens theorem S(1+x dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0).(1,3) oriented…

A: "Since, you have asked multiple questions, we'll solve the first question for you. If you want any…

Q: The curve C is the circle of radius 5 contained in the plane z 5 and centered around the z-axis,…

A: Solution:-

Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: 4- Find the length of the curves in Exercises. 1. y = (1/3)(x² + 2)³/2 from x = 0 to x = 3 3. x =…

A: for a function of the form y=f(x) length of the curve from x=a to x=b is: L=∫ab(f'(x))2+1dx and for…

Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

A:

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: 4- Find the length of the curves in Exercises . 1. y = (1/3)(x² + 2)³/2 _from x = 0 to x = 3 3. x =…

A:

Q: De termine an inter val Ca,b] on which figed pointiteration wil1 Con verge, for the equatron X= x2+1…

A:

Q: Find F. dr where C is a circle of radius 2 in the plane. x+y+z 9, centered at (4, 3, 2) and oriented…

A: Consider the given equation: And the plane x+y+z=9 centered at 4,3,2.

Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)ĵ where C is the circle x² + y² =…

A: In this we have to verify green theorem.

Q: By using Green's theorem evaluate (4.ry – y') dr + (x + 3ry) dy where C is a closed curve starting…

A:

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: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

A:

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: dz -, n = 2,3, 4, ... where z = a is inside the simple closed curve C. (z – a)" Evaluate

A:

Q: 1 4. Let f(=) =- s · Show that J (z)dz = 0 , where C is a simple closed contour not passing…

A: Moreras theorem

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is Then x…

Q: c) By using Green's theorem evaluate UTM £ (kry – y") dz + (z² +3ry) dy where C is a closed curve…

A:

Q: c) By using Green's theorem evaluate OUIM GUTM U where C is a closed curve starting from the origin…

A:

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

A:

Q: 3. Find a parameterization of the curve C= r(t) = (x(t), y(t)) a. Where C is the line segment…

A:

Q: Prove that the curve given by the equations x=R(cost+tsint),y=R(sint−tcost) is the involute of the…

A:

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

A:

Q: nath A = 30, B = 20, C = 11, D = 22. 3. Discuss how to evaluate Z enclosing the origin. dz, where C…

A:

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A:

Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: Let C be the curve of intersection of length of C from the origin to the poi

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Q: urve that lies to the left of (a) Z = - 0.45, (b) Z = 0.38, (c) Z = 0.83, and (d) Z= 1.37. mal curve…

A: According to guidelines we solve only first question when the given questions are different.

Q: Let L be the line with equation y =r- 1. Find the minimum distance between L and the point (4,5) by…

A:

Q: )مه و و ي (x2 + y?, y* + 4x) · dr (2,1) )هد0( )ه,(

A:

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

A:

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: 99. Determine the concavity of the curve x= 2t + In t, y = 21 – In t. %3D

A:

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: 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: 7. Find the area of the portion of the plane z = 2 y that lies directly above the circle x+(y-1) =1…

A:

Q: apply stok's Theorem to evaluate (Ydz +7dy+ xdz) whereCiB the curve of intersection of x²+ y²+z² =…

A:

Q: 4- Find the length of the curves in Exercises. 1. y = (1/3)(x² + 2)³/2 _from x= 0 to x = 3 3. x =…

A:

Q: c) By using Green's theorem evaluate $ (4xy – y°) dx + (x³ + 3xy) dy where C is a closed curve…

A:

Q: Covider that te curve c is an inters ecdios of the surfaces SMown below If Cirlt)= (x(t), (t), Zlt)…

A:

Q: 7. Find the area of the portion of the plane z = 2y that lies directly above the circle x +(y-1)² =1…

A: we have to find area of the portion of plane .and coverting the problem in polar coordinate makes it…