Let f (z) -Let C'be the circle z 10in the counter-clockwise direction. What is 1 -Lf(2) dz? 2ri

Q: COSTZ (iii) dz, where C is the Jc (z²-1)2 circle |z – 2| = 2 counterclockwise.

A: Let fz=cosπzz2-12 and C is the circle z-2=2 fz can be written as fz=cosπzz2-12=cosπzz-12z+12…

Q: 2x +3K Zx2 - 4x + 13

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Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 2 – 1 - lim R00 YR…

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Q: 2e Let f (2) = Let C'be the circle z| = 8 the counter-clockwise direction. (z – 4) (z – - Find |…

A: We have to evaluate the integral ∫ fzdz over the circle C which is given as z=8 and the complex…

Q: Let f (z) = SLet C'be the circle |z| = 2in the counter-clockwise direction. What is | f(2) dz 2ri C

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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: What is dyldx at the point (1,2) of xy^2 + 2xy 8 ?

A: The given equation is: xy2+2xy=8...(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: Find the equahion a Hhe tangent Lie FlX) =482- 5X +7 when R=1

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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: 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: z dz 2z ² +(1+i )z -i C is the circle |=|=2

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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. 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: dz Find an upper bound for 9c z4 –5z²+6 dz, where c is the circle |z| = 4.

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

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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: 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: 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: 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 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: 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…

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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: 4. Evaluate y ds where C is the upper half of circle x² + y² = 9, traversed in the counterclockwise…

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Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: Find the arclength of y = 2x /2 on 1 < ¤ < 3 2x3/2 uostion

A: given that y=2x3/2. we need to find the arc length in the interval [1,3] the arc length formulae is…

Q: 3. a) Compute: f (Rez-32) dz where I is a directed line segment from z=0 to z=i. b) Let C be the…

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Q: 1 Let f (z) = . Let C be the circle |2| = 2n the counter-clockwise direction. What is 2ri Lf(2) dz?…

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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: 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: 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: 3y², Compute divà and curlà for à = (x²y²z?)î – (2xy² – 16x)ĵ + (9_)&.

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Q: + 4z 53. Use (7.8) to evaluate dz around the circle |z – 2i| = 2. - z4 + 8z2 + 16

A: Given,  ∮z3+4zz4+8z2+16 dz  around the circle z-2i=2

Q: Let C be a circle with |z - i| = 3 travelled once in counterclockwise direction. Evaluate: 5z3 + 3z2…

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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: Integrate counterclockwise dz, C' the circle with z² + 8z + 15 center -3 and radius 2. dz = La z2 +…

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

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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: (a) Evaluate sin 2z dz, 3z -71 where C is an anticlockwise unit circle centred at the origin. 4.

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Q: 2e% Let f (2) = Let C be the circle (z – 4) (z – 6) 2 = 8 in the counter-clockwise direction. |2|

A: Solution

Q: Let G₁ be z = 6-√√36 - x² - y² and G2 be the upper nape of x² + y² - 3z² = 0. If S is the circle…

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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: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: Let C be the curve connecting (1,1) to (-1,-1) clockwise around the circle x2 + y = 2 1 -dy + y? + 1…

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Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

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

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