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

Q: (a) find a parametrization of the path C, and (b) evaluate (r? + y?) ds.

A: Here we have to find the Parameterization of path C, Counterclockwise around the circle x2+y2=1 from…

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

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Q: Evaluate 8 1 Ti fc 101 dz , (z+10i)³ ] z+10i where C is the circle |z+ 10i| = 1 + 8, 0 < 0 < 27 .

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

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Q: draw and identify the graph of the following surfaces a. x² + y² = sin²z, z = [0, π]

A: Any surface in the 3D plane can be represented in the form of f(x,y,z)=0. A graphing utility can be…

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: 35. In the xy-plane, the circles with equations (x-3)² +y² = 11. and (x+2)² + y² = r² |3D %3D 2re…

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

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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: Given the expression x* – 3x + 7 = y³. on the interval [3,5], determine the surface of revolution if…

A: Given; x4-3x+7=y3 on the interval [3,5]

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: Given the expression x⁴-3x+7=y³ on the interval [3,5], determine the surface of revolution if it is…

A: Given that, the expression is x4-3x+7=y3.

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: Find the center C(h,k) and radius (a) :of the circle 9. x² + y² – 4x 4 С (4, 3/2), а 3 5 О %3D C(4,…

A: The General Equation of the circle is:

Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

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: Re(z) dz, where C is the right half circle |2| = 3, from z 2² – 2i (Ъ) -3i to z = 3i.

A: To Determine :-  An upper bound of the absolute value of the integral. ∫C Re zz2 - 2i dz  where C is…

Q: Integrate counterclockwise around the circle |z – 6i| = 3. z(z – li)? - NOTE: Enter the exact…

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Q: A D E y 50 W V 20 70 В ZDCE= 90 AD = AE = AC = AB by the Hypotenuse Midpoint Theorem + Thus DECB is…

A: The given figure is- Given that AD=AE and AB=AC

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

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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: 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: 2. Use Green's Theorem to evaluate (7z +y) dy - (r² – 2y) dz where C is are the two circles as shown…

A: theorem:

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

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Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

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Q: Evaluate P (3x + 4y) dx + (2x – 3y) dy where 'C is the circle x?+y = 4.

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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: 8. Show that the circle and the ellipse are tangent to each other and draw the figure, x? + y? – 6x…

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Q: 3. Evaluate ff, (x² + y²)³/²dA, where D is the region in the first quadrant bounded by the x-axis,…

A: Given problem:- Evaluate ∫∫D (x² + y²)3/2 dA, where D is the region in the first quadrant bounded by…

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

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Q: 2.2 Prove that ne dz < 3 e 2 ++1 whore C is the arc of the circle 2| = 3 from z = 3i to z = -3. %3D

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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: 8. Use the diagram of circle H to find JK if DG = 24 and FH=I %3D G. JK = D 7, F.

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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 diagram below, O is the centre of the circle. CDE is a tangent to the circle at D. DB bisects…

A: Solution as follow

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: 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 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: (3²+ 3a)dA, where D is the region in the 3rd quadrant between the circles 2² + y² = 1 and x² + y² =…

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Q: Show that = sin t if t>0 and C is the circle z] = 3. 2mi Jz+1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: In the circle below, suppose m KLI = 124° and m LKJ=46°. Find the following. %3D (a) m ZKLI %3D (b)…

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Q: in R°sketch the graph of the cylinder x = (y – 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: 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: Find an upper bound of the absolute value oI e +1 (a) dz, where C is the right half circle |z| = 3,…

A: Note:  Since you have posted multiple questions, which are independent, as per our policy we are…

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…