Compute cos(z) √o z² - 6² +5 where C is the positively oriented circle of radius 4 centered at the origin. . dz,

Q: Use the Theorem of Pythagoras to find the length of the line segment y = 3xfrom (1,3) to (2,6), and…

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Q: Let C be a positively oriented unit circle. Compute the residue of the following: (a) f(z) = z(z²+4)…

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Q: d Fill in the chort: use 3 2 lost 2 coso -) 30° 60° 120 180 240° 2300 3000 230° 160

A: The solution is given below

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

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Q: A circle with center at the origin and radius equal to a meets the axis of x at A and B. P(a) and…

A: The coordinates of A are (-a,0) and that of P are (a cos α,a sin α)  Therefore,the equation of AP…

Q: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

A: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

Q: X. Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1,-1) to (0,0), C₂ is the line segment…

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Q: 1 € /₁ (2² + 1)2 dz. Let C be the circle |zi| = 1. Evaluate

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Q: Prove that for every real number x, if x > 1 then there is a real number y such that y+ý = 2x.

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

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Q: Let F (x, y) = 8Q A. Compute 82 yi+zj z² + y² and let C be the circle r(t) = (cost)i + (sin t) j. 0…

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

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

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Q: =2) Calculate & ydx + xz² dy - zy³ dz, where c is the circle x² + y² = 4, Z=3 (conterclockwise)…

A: We will use stokes theorem to find integral

Q: 1. Use Green's Theorem to evaluate |F. dr, where F(r, y) = (3y- esin, 7x + Vy + 1) and C is the…

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Q: Prove that the angle between the tangents from (a, ß) to the circle x² + y² = a² is 2tan ¹(a/√S),…

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Q: Find the cosine of the angle between the following two planes. -1x -4x cos 0 = [3]/[2(sqrt(15))] +2y…

A: -x+2y+5x=-1-4x+3y-5x=1

Q: 5. Find the total length of the curve r-4 (1-sin e) from 0-90° to 0-270° and also the total…

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Q: M2. Let C be the positively oriented circle |z1|-2 in the complex plane. Which of the following is…

A: Given C is the positively oriented circle  in the complex plane. We need to find the value of line…

Q: Find the lengths for the (r= θ² , 0 ≤ θ ≤ √5)

A: Arc length

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

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Q: Q3) +4ƒ=0,0≤x≤1.0 ax² Subject to the boundary conditions: f(0)=0 f(1) = 1

A: We have to solve the differential equation .The boundary condition is

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

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Q: TC is a tangent to a circle at C and BA produced meets this tangent at T. Show that triangles TCA…

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Q: Evaluate 1 2. tht Htte tan e(:-+) 2 , у акуся, whve с is the contour given by

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

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Q: If a circle passes through the point (0, 0), (a, 0) and (0, b), then find its center. Prove that for…

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Q: A circle with center at the origin and radius equal to a meets the axis of x at A and B. P(alpha)…

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