Let D be the circle |z| = 3, oriented counterclockwise. For any positive integer n compute the contour integral Your answer should depend on n. n +1 L ( == 2)" d= dz

Q: the circle is the tangent to both x and y axis. A point on the circle is (2,1). Calculate the area…

A: This question is based on Circle.

Q: Find x so the distance between (x, 3) and (4, 7) is 2/5.

A: Answer

Q: Is GH tangent to circle Fin the diagram below? 41 40

A: The given diagram is:

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

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Q: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

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Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: 5. Sketch the circles x + y = why the circles must be internally tangent. (Hint: Find the two radii…

A: Given: i. x2+y2=225ii. x-62+y-82=25 To Find: Sketch the given circles and explain why the circles…

Q: Let C be the upper half (yzo) of the circle x² + y2 = 16 from (4,0) to (-40). √ (ax 2-3y) ds =

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Q: Evaluate 12x-7 dz where (2213) (2-1)² Cis the circle Z = 2

A: Approach to solving the question:  Detailed explanation:

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

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

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: Compute с -ater-clockwise see from above. where xdy - y dx ус is the unit circle center at origin…

A: Introduction: In vector calculus, another very important theorem is Green's theorem. It makes a…

Q: Evaluate (r2 + y?)ds, C is the left half of the circle with radius 4 centered at (0,0) and is…

A: We calculate this by using concepts of line Integrals !

Q: 6a) Let A be the parabolic arc defined by the equation y = 8x – x´ over the domain interval [0, 8].…

A: (a) Consider the given function. y=8x-x2 Now, draw the above function by using the calculator.

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: Find the length of the curve r = 02 from 0 = 0 to 0 = 14.

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Q: Let F(x, y) == and let C be the circle r (t) = (cost)i + (sint)j, 0 ≤ t≤ 2π. A. Compute მი Note:…

A: Step 1: Step 2: Step 3: Step 4:

Q: 2. Circle One. Are (x-3) and (x-2) factors of: f(x) = x'-3x -4x+12 YES or NO

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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: ort er 2x² + 2y² + 4x + 8y + 8 = 0 is the equation of a circle with center (h, k) and radius r for:…

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Q: 3. Use the Secant method on the circle function (x + 1)²+(y – 2)²= 16 to %3D find the intersection…

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Q: Find the area of the circle whose center is at (2, -5) and tangent to the line 4x+3y-8=D0

A: Area of the circle = 9π sq.units

Q: Find the area of the surface generated when the given curve is revolved about the given axis 1 = (e…

A: Given y=112e6x+e-6x  ,for -2≤x≤2  Area of surface of curve when revolved about x-axis…