Use spherical coordinates to evaluate // | eva*+*** dV, where E is enclosed for E by the sphere x² + y? + z² = 9 in the first octant. 1. (9e³ – 1) 3 2 2. (5e – 2) - 2 3. 2т (9е — 1) 4. 27 (5e° – 2) 9T 5. 2 3

Q: 2. Use Green's Theorem (and only Green's Theorem) to evaluate |(2? + y)dx + (x² – y³)dy, where C is…

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Q: 9. Calculate lim (2,y,2)→(0,0,0) x² + y² + z² by converting to spherical coordinates.

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Q: √4-j2 217 0/ convert the integral (SS Srdzr drdo) to rectangular coordinates and Spherical…

A: Here we can note that the given integral is in cylindrical coordinates. Also rectangular coordinates…

Q: The surface 10x – 9y = z2 can be described in spherical coordinates in the form p = f(0, 4) help…

A: Given 10x-9y=z2

Q: Match the surface to its corresponding equation in spherical coordinates. |p = 4 cos() 1.5 -1 -0.5 0…

A: To match the given surface to their given Equation in spherical coordinates.

Q: 31. Use sine and cosine to parametrize the intersection of the surfaces x² + y² = 1 and z = 4x²…

A: Given x2+y2=1 & z=4x2 x2+y2=1 is the equation of circle. That is x2+y2=12,  Therefore, Radius is…

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

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Q: Use spherical coordinates. Evaluate ∭z dV, where E is between the spheres x ^ 2 + y ^ 2 + z ^ 2 = 16…

A: Triple integral is used to integrate function of three variable in three dimensional region.

Q: Find the radius of curvature at 0 = t of the parametric equations x = 3(0 + cos 0), y = 3(1 – cos…

A: To find the radius of curvature, first find out dxdθ and d2xdθ2. x=3θ+cos θdxdθ=31-sin θd2xdθ2=-3cos…

Q: Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.

A: Given, the cylinder                         We have to find a parameterization of this given…

Q: 15. Find the radius of curvature at 0 = -n of the parametric equations x = 3(0 + cos 0), y = 3(1 –…

A: For the parametric curve x=x(θ), y=y(θ)Curvature K=|x'y''-y'x''|[(x')2+(y')2]32Radius of…

Q: Which of the following surfaces cannot be described by setting a spherical variable equal to a…

A: Given,ρ=k , ϕ= k , θ=k To check which one of the given surfaces cannot be described in the above…

Q: 4. Use cylindrical coordinates to evaluate [!] √²³² + y²dv₁ D where D is the region that lies inside…

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Q: 15. Find the radius of curvature at 0 = ÷n of the parametric equations x = 3(0 + cos 0), y = 3(1 —…

A: Given two parametric equations, x=3(θ+cosθ),y=3(1-cosθ) To find the radius of curvature at θ=π3

Q: Exercise 3.2.10. Using K = (In - m²)/(EG – F²), show that the Gauss curvature of the R- sphere S²(R)…

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Q: Which of the following are parametric equations for the ellipse given by + y? 9 1? Choose all that…

A: Idea: By using parametric equation of ellipse we can solve this question .

Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: Find an equation of the form p = ƒ (0, 4) in spherical coordinates for the surface z = 16 (Use…

A: The equation in spherical coordinates for the surface is determined as shown below

Q: By transforming into spherical polar coordinates, evaluate JJ) 1-x². ff - (- dxdydz , taken…

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Q: Use spherical coordinates. Evaluate (x2 + y2) dv, where E lies between the spheres x² + y2 + z² = 9…

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Q: Use spherical coordinates. Evaluate |/| (x2 + y²) dv, where E lies between the spheres x2 + y2 + z2…

A: For spherical coordinates: x = ρ sinφ cosθ, y = ρ sinφ sinθ z = ρ cosφ. So,       x2+y2=ρ sinφ…

Q: dv Use spherical Coordinares to compute H 2 where W is the solid bounded by the spheres 4 ty+z² =g…

A: Given I=∫∫∫wdVx2+y2+z2Where W is the solid bounded by the spheres x2+y2+z2=9 and x2+y2+z2=4.

Q: (a) Let D be the region enclosed by the surfaces z =- |4–x² – y² and z= +y² . Determine zdv by using…

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: Let N be the lower hemisphere of the sphere of radius 5 and let H • Construct dS for 2. Try using…

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Q: The surface 22 = x² +y? – 4x + 5 remains unchanged when rotated about the line L in R³ Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

A: Consider the equation of circle

Q: Use spherical coordinates. SI. Evaluate Vx2 + y2 + z2 dV, where E lies above the cone z = Vx2 + y2…

A: The spherical coordinate system is a polar coordinate system used to translate cartesian plane to…

Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z² = 1 and x2 +…

A: Using spherical  coordinate we can solve it very easily.

Q: 29. Find parametric equations for the tangent line to the cur ve of intersection of the paraboloid z…

A: Given paraboloid is z=x2+y2 ellipsoid is x2+4y2+z2=9 and the point (1,-1,2) find the parametric…

Q: In spherical coordinates, the integral •√√4-x²-y² IMM x² /4-22 None of these. 2π *π/2 2 S √²* [*¹²*…

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Q: 3. Consider the parametric vector equation of a cone r(u, v) = u cos vi + u sin vj + uk with 1<u < 2…

A: The volume  of a cone with radius r  and height  h is given by  V=13πr2h.   Given a  function…

Q: 9.) Find the flux for F(x, y, z) = xi + yj + zk and S: x + y? + z? = 9 in the irst octant. (Hint:…

A: Flux problem....

Q: 9. (a) Find the equation of the cone 3.x2 +3y2 in spherical polar coordinates. (b) Use spherical…

A: Given

Q: Find the center C and the radius r of the sphere S: x2 + y2 + z2 + 4x + 8y – 8z =-11

A: A geometrical object which is in the shape of ball is called sphere. Outer surface of sphere is…

Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z2 = 9 and x2 +…

A: Given equations of spheres: x2+y2+z2=9 x2+y2+z2=36 For spherical coordinates: x=ρ cosθ sinϕy=p sinθ…

Q: 3. Find the moving trihedral and the curvature at any point of R(t) = (In(sect), t/V2,t/V2). %3D

A: Introduction: In differential geometry, the Frenet–Serret formulas define the kinematic properties…

Q: Use spherical coordinates to evaluate the triple integral [[[ 2² + 3² + 2²dV, where E is the ball:…

A: We will first change it into spherical coordinate and then solve it.

Q: Gz find the Velume of the Selid with in the cylinder xya16 and between the y-2-3 and Z=2(polar)…

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Q: onvert T (=² + y² + z®) dzdzdy into spherical coordinates. /4 /3 /2 2/2 - 2×/3 /2 -2/2 /4 /2 2/2 /2…

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Q: 1. Identify the parametric surface S given by: r(u, v) = 3 cos ui+ vj + 3 sinu k where 0 <u < 2n and…

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Q: c) Use spherical coordinate to evaluate x dz dy dr 4-x²-y²

A: Sketch the region and find range of variable

Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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Q: # 2. Let C be the curve that is the intersection of the cylinder x²-2x+4y2 = 0 with the plane z-x…

A: The cylinder x2-2x+4y2=1 and a plane z-x=3. We have to find the parametric equations for the…

Q: A solid lies above the cone z = V x² + y2 and below the sphere x2 + y2 + z2 = z. Write a description…

A: We have, z=x2+y2            ⋯⋯1 Let us consider, x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ On substituting in…

Q: 17. Let T be the solid bounded below by the half-cone z = Vr2 + y? and above by the spherical…

A: Consider T be the solid bounded below by the half cone z=x2+y2 and above by the sphere x2+y2+z2=1.…

Q: 6. Find the projection of u = -7 onto the -2 line e of R given by the parametric equation l = tũ, -1…

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Q: (2) Write parametrizations 7(u, v) for the following surfaces (a) a sphere with radius 5 (b) a cone…

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Q: #1. Find a parametric representation of the part of the cylinder x² + z? = 9 that lies above the…

A: parametric equations for a cylinder of radius 3 x^2+y^2+z^2=r^2 Where r=3

Q: Given the cylinder (M): (x + 1)² + (y – 1)² = 2. (M) can be presented in cylindrical coordinates as:…

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