Use cylindrical coordinates to evaluate the triple integral SSS √x² + y² dV, where E is the solid bounded by E the circular paraboloid z = 1 − 16 (x² + y²) and the xy-plane.

Q: The horizontal tangent plane of the surface z = 2x² – xy – y² + 6x – 6y – 2 is given by the equation…

A: Consider the given equation. z=2x2-xy-y2+6x-6y-2 Find the derivative with respect to x and y.…

Q: At what point on the paraboloid y = x² + z² is the tangent plane parallel to the plane 3x + 2y + 3z…

A: Introduction: Let z=f(x, y) be the equation of a surface S in R3, and let P=(a, b, c) be a point on…

Q: luate the surface integral. // (x + y + z) ds, S is the parallelogram with parametric equations x =…

A: Sub x= u+v  y= u-v  z= 1+2u+v

Q: Evaluate /|/. x dV where E is the solid enclosed by the paraboloid x = y²+z² and the plane x = 9

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Q: Find the surface area of the solid obtained when the parametric curve x = −2cost; y=2sint for 0 ≤ t…

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Q: The temperature adjusted for wind-chill, w, is a temperature which tells you how cold it feels, as a…

A: Answer:- s=10; Independent variable=T= 35 30 25 20 15 10 5 0 Dependent variable=ω= 27 21 15 9 3…

Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

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: Find the surface area of the part of the plane z = 2x - y − 3 that lies inside the - cylinder x² +…

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Q: Evaluate the surface integral. J[x (x + y + z) ds, S is the parallelogram with parametric equations…

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Q: Evaluate the triple integral z dV, where E is enclosed by the paraboloid z= 4x2 + 4y2 and the plane…

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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: Use Stokes' theorem to evaluate V ×F· î dS where = (9y²z, 4xz, 2x²y²) and S is the paraboloid z = x²…

A: Step:-1 Stoke's Theorem:- ∬s∇×F→.n dS=∫F.dr Now, given that F→=9y2z, 4xz, 2x2y2 and paraboloid…

Q: Evaluate the triple integral J20² S 2x²z + 2y²z dv where S is the solid that lies below paraboloid z…

A: Given integral: Where  is the solid that lies below paraboloid  and above plane