If F= 2y I- 3J +x²k and s the surface parabolic cylinder y= 8x in bounded by the planes OF the 2. the Ferst octant Y = 4 and 2 =6, show that F.Nds=132. S,

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: Evaluate the line integral xyz ds where C is the line segment joining the points (1, – 1, 1) to (1,…

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Q: Find a point on the surface x - yz = 11 that is closest to the origin. (a, ± √b, √c), where a ,b= =…

A: We have to find the point on the surface x-yz=11 that is closest to the origin.

Q: (x² + xy) dx + (y² - xy) dy; C: the line y = x from the origin to the point (2, 2).

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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: Determine the point(s) on the surface z = e(3x² +9y2) at which the tangent plane is parallel to the…

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Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

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Q: et F(x, y) = (y sin x)i - 3x²j. et D be the unit square (i.e. D = {(x, y): 0≤x≤ 1,0 ≤ y ≤ 1}), and…

A: We have to choose the correct answers of two questions.

Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

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Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

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Q: Solve using method of undetermined coefficients: y" + y' - 2y = x². %3D

A: Solution :-

Q: I, Use Stoke's theorem to evalueate S.Fidr, where F Cau2)= - it +x3 + 2î aind C is the Ceurve of…

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Q: Suppose that the plane tangent to the surface z = f(x, y) at (2, 7, 8) has equation z + 8x – 2y =…

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Q: Evaluate the length of the curve x = 6 – Vy – 2 , 3< y<6

A: To find the length of following curve  x = 6 - sqrt( y - 6) 3 ≤ y ≤ 6

Q: line integral x³ dy), where y is t 3 X counter clockwise.

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Q: Let C be the curve consisting of line segments from (0, 0) to (1, 1) to (0, 1) and back to (0, 0).…

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Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

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Q: Consider f (x, y) 3x² + xy + 3y². Use calculus to find the extreme values of fon the circle x² + y²…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: We have to use Langrages Multipliers Method to find the minimum distance from (0,c,0) to a point on…

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A: A tangent plane to a surface is a plane that just touches the surface at a single point. The…

Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

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Q: The level curve of the surface f(x,y) = x² + y2 + 4x -10y + 28 corresponding to c is a circle of…

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Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

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Q: The equation of the tangent plane to the surface ye+z 0 at the point (0,-1,1) is az+by+cz 1. Which…

A: If  F(x, y,z)=0 is a three variable real valued function and generates the surface S, then the…