3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0

Q: Let F = (7z+7x4) 7 + (3y + 2z + 2 sin(14)) 7 + (7x + 2y + 3e²¹ ) k. (a) Find curl F. curl F = (b)…

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Q: Find the circulation f V. dR, where V = yi + (x² + y²)j + (x + y)k, and C' is the triangle with…

A: In this question we will find the circulation of

Q: 2. Let l be the line x² + y² − 4x + 2y +1 = 0 and drop a perpendicular from O to Q E l. (a) Explain…

A: Step 1:Part (a): Finding the coordinates of (Q), where a perpendicular is dropped from the origin (…

Q: [2] [Derivation of Simpon's Rule] In this exercise will derive Simpson's rule using Taylor's…

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Q: Tangents are drawn to x² + y² = 1 from any arbitrary point P on the line 2x+y-4 = 0. Prove that…

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Q: Let a b and n Let A- (a.az, as), B- (b. b, ba).S- conv (aa a) and T-conv (b, by, by). (a) Find a…

A: Answer for sub question 1: Given: a1=2-15, a2=313,a3=-160,b1=05-1,b2=1-3-2,b3=221,n=31-2 To find…

Q: Let f(z) = x? + iy² where æ and y are the real and imaginary parts, respectively of z and C is a…

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Q: Let C2 be the boundary of the triangle whose vertices are (1, 2), (-3, 1), and (-2, 2). Suppose C2…

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Q: Let C be the closed curve oriented in the counterclockwise direction, consisting of the line segment…

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Q: Suppose that we start at the origin in the xy-plane and take n unit steps (i.e., each step is of…

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Q: Find the points on the graph of z = xy³ + 8y-¹ where the tangent plane is parallel to 8x + 5y + 8z =…

A: The given curvez=xy3+8y-1Let F(x,y,z)=xy3+8y-1-z∇F(x,y,z)=(y3,3xy2-8y2,-1)Hence, the gradient at…

Q: Use the Cauchy-Riemann PDES to determine all points z =z+ iy € C in which the following functions…

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

Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: P1=(x1,y1,z1) and P2=(x2,y2,z2)  prove that distance of P1 and P2 ; |P1P2|=((x2-x1)2 +(y2-y1)2…

A: Solution: The objective is to prove that the distance of P1 and P2   |P1P2|=((x2-x1)2 +(y2-y1)2…

Q: Find the maximum value of f(z)| = |z²+ 3z - 1| on the unit disk |z| < 1.

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Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

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Q: Consider the following. C: line segments from (0, 1) to (0, 4) and (0, 4) to (3, 3) (a) Find a…

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Q: Find (d/dz)2coshz using principal values. Where in the complex z-plane is analytic?

A: We have to find the derivative of 2cosh⁡(z) with respect to z, we can use the chain rule along with…

Q: How Find of and Duf to:- -3 f (x₁Y,Z) = 27²³²—3 (x² + y²³) Z + tań X Z on the point (1,1,1) in the…

A: The given function is