In the following exercises, the function f and region are given. a. Express the region E and the function f in cylindrical coordinates. b. Convert the integral B f (x, y, z) dV into cylindrical coordinates and evaluate it.

Q: Use cylindrical coordinates. Evaluate √x² + y² dv, where E is the region that lies inside the…

A: The region lies inside the region x2+y2=4 and between the planes z=-5 and z=-2. We have to evaluate…

Q: Find the unit tangent, normal, and binormal of the following parametrization: c (t) = (4cos3t,…

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Q: Find the area of the surface with the following parametrization: u COS V Τ (u, υ) - u sin v u? 0<u<…

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Q: SS. F.n do across the surface in the given direction. Use a parametrization to find the flux F =…

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Q: Solve for the value of "b" in the equation: * (12) + b 11 Your answer

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Q: lies between the cylinders x2 + y² = 4 and x² + y? 2 2 6 above the xy-plane and below the plane z =…

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Q: r4–x²-y² x²y dz dx dy /2-y² Jx²+y² x² + y² by converting to cylindrical coordinates.

A: We will evaluate the given integral.

Q: Determine the y-coordinate of the centroid of the shaded area. b 1 x=y²/b 0.63b

A: Consider the following figure. Equation of straight line is y=1−0.63x=0.37x. For a thin strip…

Q: :f (x, y, 2) = x + y; E = {(x, y, z) |1 0, y > 0}

A: In this question given that a function and it is in the cartetion coordinate. We can convert in…

Q: Use a parametrization to find the flux F.n do across the surface in the given direction. F= - xi -…

A: The electric flux through a surface depends only on amount of charge enclosed by the surface. It…

Q: 2. Change Vx? + y? dz dy dx into cylindricalcoordinates, then evaluate. J-1 Jo

A: Given I=∫01∫-1-x21-x2∫x2+y22-x2-y2x2+y2 dz dy dx

Q: Use cylindrical coordinates to evaluate V9-x² r9-x²-y² a² dz dy dx -3 J- 9-x² Jo Do not forget to…

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Q: c) cosh(2 + j3) d) csch 1 + j (₁ + ; ²7/1) 3.

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Q: (2² + y²)dV, where D is the solid that lies Use spherical coordinates: Evaluate above the xy-plane…

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Q: Use cylindrical coordinates to calculate : x? + - y dV W : x + y < 25, 0sz<4 SII»(x² + y² ) dV =

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Q: Use spherical coordinates to evaluate fff (9-x² - y2) dV where E is the solid hemisphere E x² + y2 +…

A: To Evaluate: The integral ∫∫∫E9-x2-y2dV where E: x2+y2+z2≤9 , z≥0 using spherical coordinate system.

Q: Describe the bifurcation for the following dy - Ay - y %3D dt

A: The saddle node-bifurcation: Let y˙=f(α,t) is the system of equation, the to find the saddle-node…

Q: Use cylindrical coordinates. Evaluate JIS. √x² + y² dv, where E is the region that lies inside the…

A: Evaluate the integral.

Q: The Lagrange multiplier technique is to be used to find the points on the ellipse 2r² + y² = 1…

A: The Lagrange multiplier technique is to be used to find the points on the ellipse  closest to and…

Q: a) Find a scalar function f such that F= Vf where F(x,y) = (3 + 2xy²) i +(2x²y)j.

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

Q: Evaluate II| 6x(x2 + y2) dv, where E is the solid in the first octant that lies beneath the…

A: Since the integral lies in first octant so 0≤θ≤π/2 and z≥0.  Converting into cylindrical coordinates…

Q: Express the rate of inflation from 1985 to 2015 as a percent correct to two decimal places. Year…

A: To find - Express the rate of inflation from 1985 to 2015 as a percent correct to two decimal…

Q: Use cylindrical coordinates. Evaluate II V + 2 dv, where E is the region that lies inside the…

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