Consider the solid D that lies inside the cone, and bounded below the plane, :=-4. Set up the triple integral for +y?+z)dV in spherical coordinates.

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

Q: Use spherical coordinates to evaluate 2π FT S 2-r r+z 0 (r² +2²) ³/ rdz dr de.

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Q: Q3// B Verify that dv3p'sin Ddpd@d owhen using spherical coordinate

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Q: Use spherical coordinates. Evaluate (8 - x² - y²) dv, where H is the solid hemisphere x² + y² + z² ≤…

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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: [₁ F. dr where F = , and C is the circle of radius 5 centered at Evaluate the origin parametrized in…

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Q: Convert this integral from rectangular coordinates to cylindrical coordinates (Do not evaluate the…

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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: 2. Sketch the cylinder y = x² +1.

A: complete graph provided below with python code Explanation:  code behind above :  import numpy as…

Q: Evaluate e dz where C is the line segment from 0 to 2+2i, parametrized by z(t) = t + it?.

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Q: Find a parametrization of the surface x³ + 15xy + z² : = 10 where x > 0 and use it to find the…

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Q: Find a parametrization of the circle of radius 6 in the XY-plane, centered at the origin, oriented…

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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: a) Find the surface area of the object obtained by rotating x = e2y , –1 <y <1 about the y – axis.

A: We have to find the surface area of the solid obtained by rotating the curve x=e2y about the y-…

Q: Explain why C lies on the surface of the cylinder x² + y² = 1.

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Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

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Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: parametrization of the surface z = 3x² + 8x, ymbolic notation and fractions where needed.

A: In this question, the concept of the tangent plane is applied. The equation of the tangent plane of…