evaluate the integrals around the circle Iz| = 2, counterclockwise. 9) 1 = dz, Find |I| 4z2+9 z+1 8) 1 = dz. Find |/| z+i 10) I = sin z dz, Find |/| z3+z2

Q: Q3] Find the value of contour Integral if C is the circle |z1| = 1 e²z dz z3z² + 4z - 4 C

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Q: Sketch the triangle with vertices O, P = (0,7, 3) and Q = (7,4,0) and compute its area using cross…

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Q: х? — бх + у? — 2у - 6 %3D 0

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Q: Q₁) Find Jz dz 1. along the contour integral c from 1+i directly to 3+i3? 2. along line from 1+i…

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Q: Find the equations of the normals to the circle x² + y² − 8x – 2y + 12 = c a t the points whose…

A: Solution:- Given circle is x2 + y2 - 8x - 2y + 12 = 0 Putting the ordinate, we get the abscissa…

Q: Line segment AB is a diameter of the x² +y² + z² - 2z + 8y = 9. Find point B if A = (0, у, 0).

A: To find the point B if Coordinates  of A are given for the sphere.

Q: 20. Find curl(F), where F(x, y, z) = xyz¹i+x²zªj + 4x²yz³k. a) (-4xyz³)j + (xz¹)k b) x²yj+xz¹k 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: Show that 25+ 2z² + 3z + 2 has five zeroes inside the circle |z| = 2, and determine the number of…

A: If f(z) and g(z) are two analytic functions within and on a simple closed curve C such that |f(z)|…

Q: с Solve for D B Same point B 130 A LACB LCBD LABD с сва Using circle Theorem.

A: Given information:  Aim:   Using Circle theorem.

Q: solve for no. 4 and 5

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Q: Where an Interior point Exists?

A: Interior point: Let S⊆ℝn.  A point a∈ℝn is said to be an Interior Point of S if there exists an…

Q: b) - a +b-c+d = 0 – 2a + b+c-3d = 0 a + 2b - 3c + d = 0 2a + 3b +4c- d 0

A: Let us considre the system of matrix Ax=b Using Cramer's rule, the solution of the system of…

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 the double integral 1+ 4x² + 43²&A where D is the bottom half of the circle x? + y? = 16.…

A: In polar coordinates,                                   and

Q: 323 + 4z2-5z+1 dz (z-2i)(23-2) 1. Compute: where C = {|z| = 3} is the circle of radius 3 centred at…

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Q: Integrate h(x, y) = (x+y)i + (y²-x)j over the closed curve that begins at (-7,0), goes along the…

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Q: In each case, determine if ₁ and ₂ are parallel, perpendicular, or neither. Explain. a) ₁: 4x-6y=9…

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Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

A: (1)    Given that the equation of the circle is   x2 + y2 - x - y - 6 = 0                Given point…

Q: Sketch the triangle with vertices O, P = (7, 0, 7) and Q = (3,0, 3) and compute its area using…

A: To find the area of the triangle using cross product method when it's vertices are given .

Q: Q4. equation of circle x² + y² - 6x-2y +6 = 0 2 )2 (x-3)² + (y-13² = 4 circle with center line y =…

A: Note: As per your request, the solution is in digital format is given below.   Q4.  Equation of…

Q: The figure satisfies the Midpoint theorem for a triangle. Calculate (x + y) 4у x + 4 6(у-1) 4x -2

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Q: The solution of the linear congruence 4x = 5(mod 9) is? 6(mod 9) 10(mod 9) Qmod 9) 8(mod 9)

A: Since, x = 9 n + 8 and n element Z Now,  4x congruent 5 mod 9 implies  x congruent 8 (mod 9).

Q: • Graph f (x) = x° + 3x² + 3x + 3 using -2, and the interval -2, –1.7], find each of the following…

A: There is a change in every function. When the variable moves, it is obvious that the function also…

Q: Derive a cubic spline with natural boundary condition using the following points: (−2, 1), (0,0),…

A: Sol:-] To derive a cubic spline with natural boundary condition, we need to find the cubic…

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: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: Prove that the length of common chord of the two circles x + y² + 22x + c = (2² -c)(µ² +c) 2² + µ? O…

A: We will prove that the length of the common chord is the given term as following.

Q: A secant to two congruent circles, which is parallel to the line of centers OO', meets the first…

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Q: 1) Find area inside the circle r 4cose and to the right of line r = sece %3D

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 3. Use Green's Theorem to show that to where C is the unit circle x² + y² = 1 in the…

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Q: Find the total area of the shaded region below. y y = sec?t 2 1 21 - 3 3 y = -4sin?: -4

A: Solve the following

Q: What are the four main end points to the circle x2+y2-10x+8y+25=0 (show work)

A: Question is solved.

Q: Find the image of the circle /z/ 4 under f(z) = Lnz %3D 5-(15pts) Evaluate S-3/2

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