Calculate [] S F.ds where F = (3xy², xe², z³) S is the surface of the solid bounded by the cylinder y² + ² = 25 and the planes x = -2 and x = 4

Q: 5. Consider the surface: x(u, v) y(u, v) z(u, v) where u € [0, 1] and v € [0,2]. Calculate the area…

A: Introduction: The area is the area occupied by a two-dimensional flat surface. It has a square unit…

Q: ermine the point(s) on the surface z = 30x - 28y - 5x² - 7y² at which the tangent plane is parallel…

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Q: Let F= (0,0, z) and S be the part of the paraboloid z = x² + y² between the plan z = 1 and 2 = 4,…

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Q: The equation of the tangent plane to the surface 32 = x² + y² +1 at (-1,1,2) is O A.-2x-2y+3z = 2 O…

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Q: effF.d5 where F-dS Calculate F = (4x³z, 4y³z, 32¹) and S is the surface of the solid bounded by the…

A: The given problem is to evaluate the given surface integral of the given vector field over the given…

Q: Let S be the portion of the plane 2x + 3y + z = 2 lying between the points (-1, 1, 1), (2, 1, −5),…

A: S is the portion of the plane 2x+3y+z=2 lying between the points (-1, 1, 1), (2, 1,-5), (2, 3,-11)…

Q: Find the equation for the tangent plane to the surface x-9xyz +y= - 11z at the point (-1,-1,-1). O…

A: The given surface is x2-9xyz+y2=-11z2 and the point is -1,-1,-1.

Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5…

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Q: Find the sum of the x-intercept, y-intercept, and z-intercept of any tangent plane to the surface…

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Q: Consider the function f(x, y,z)=x² - y² - z² + 4x+2z+4. a. (i) Sketch and describe the level…

A: given function fx,y,z=x2-y2-z2+4x+2z+4 claim- (i) sketch and describe the level surface for f=0 and…

Q: 17. Iff is bounded and integrable on [a, bl, then IF| is also bounded and integrable on [a, b] and…

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Q: Graph the solid that lies between the surface z= 2xy/( x2 + 1) and the plane z =x + 2y and is…

A: Given surfaces are z=2xyx2+1, z=x+2y  and are bounded by planes x=0 , x=2 , x=-1 , y=0 , y=4. To…

Q: Find the points on the surface 1x² + 1y² + 3x² = 1 at which the tangent plane is parallel to the…

A: We know that two planes are parallel if their normal vector are parallel. That is their, gradient…

Q: Evaluate F.ndS for the given F and o. (b) F(x, y, z) = (x² + y) i+ xyj– (2xz + y) k, o: the surface…

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Q: Find the flux of F = z²k upward through the part of the sphere æ² + y² + z² = a² in the first octant…

A: Given vector field is  F=z2k to find the flux through sphere x2+y2+z2=a2 in the first octant.

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: Let F = < 4x + y², 5y + z, 9z + x So F. dī, Use Stokes' Theorem to evaluate C where C is the…

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Q: Calculate F - dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: Given F¯={exsiny,excosy,yz2)

Q: Find the point on the surface r – 2xy + 2y² – x+ y = 0 closest to the point (1, 2, –3).

A: Consider the provided question, We have to find the point on the given surface closest to the point…

Q: /|F . d5 where Calculate F = (3zy°, ze", 2ª) Sis the surface of the solid bounded by the cylinder y?…

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Q: Use hyperbolic functions to parametrize the intersection of the surfaces x² - y² = 25 and z = 5xy.…

A: Here we have to parametrize the surface using hyperbolic functions.

Q: Let the surface xz – yz³ + yz? = 2, then - the equation of the tangent plane to the surface at the…

A: Equation of tangent plane of the surface f(x,y,z) =0 at (x0,y0,z0) fx (x0 ,y0 ,z0 )(x-x0) +fy (x0…

Q: Evaluate | F-dS, where F(x, y, z) = (3y, –2x, –), %3D and S is the surface that is composed of the…

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