14 Find the surfuce area the part of the parabolic cy linder 2=y? that the triangle with vertices xy-plane. of lies over (0,0), (0,1), (4,1) in the

Q: Find the area of the surface. The portion of the plane z = 24 - 3x - 2y in the first octant

A: ⇒Given:-  Equation of plane                      z=24-3x-2y  in 1stoctant In intercept form,…

Q: he region Rin the first quadrant of the æy-plane is boundec A solid S is formed by rotating R about…

A: Given that The region R in the first quadrant of the xy - plane is bounded by the curves,…

Q: C:1-1,4), (1,2) (-レ-1),(ル-) the boundary of the rectonale that accepts points as a corner…

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Q: Find the extreme values of ƒ(x, y, z) = x - y + z on the unit sphere x2 + y2 + z2 = 1.

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Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

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Q: 2. (a) Use Pythagoras' theorem to find the length of the line segment y = 2x from (1, 2) to (2, 4).…

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Q: 5. Find equations for all the planes that intersect the y-axis at y = 1 and the z-axis at z = 2, and…

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Q: tind the absolure maxima and minima unction onD where D iS the closed rucie triangular region with-…

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Q: (c) Use Green's Theorem to evaluate (3xydx+ 2xy dy, where C is a counterclockwise oriented…

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Q: Find the surface area of the part of the surface z=x^2+3y that lies above the triangular region T in…

A: According to question, Given surface, z=x2+3y

Q: 12.6- Surface Area 1. Find the area of the part of the surface z = 1+ 3x + 2y²that lies above the…

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Q: of the paraboloid 2= l-x²-y² +hat Find the area of the Part The paraboloid z= -x?-y? +hat lies

A: The given paraboloid is -  z = 1-x2-y2 We have to find the area of the part of the given paraboloid…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. x3/2, 0sxs 21 y

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Q: 1-12 Find the area of the surface. 1. The part of the plane x + 2y + 3z = 1 that lies inside the…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: x (b) Hyperbolic paraboloid. M: z = a Show that M is covered by the single patch х(и, v) — (а(u+ v),…

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Q: (a) Find the minimum and maximum xcoordinates of points on the cardioid r =1−cosθ.(b) Find the…

A: given,       the cardioid r= 1-cosθ

Q: B. In a focused multicolored image of a tablecloth: Given: AE = BE and AD = CD Prove: CB || DE…

A: We know that,  By mid point theorem : A line segment between two mid point of any  Two sides of a…

Q: Find the area of the surfaces The portion of the cone z = √x2 + y2 that lies over the regionbetween…

A:

Q: 15. Integrate G(x, y, z) = z – x over the portion of the graph of z = x + y² above the triangle in…

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Q: The planex/2 + y/4 +z/3 = 1intersects the x-, y-, and z-axes in points P, Q, and R. Find the area…

A: Given: x2+y4+z3=1

Q: 1) Find the vohume of the region bounded by the Z = 2 - 4x2 - 4y² and the plane Z-0 (Note : Use…

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Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

Q: Complex Analysis

A: to test the function u(x,y) for harmonic condition, and if so,find its harmonic conjugate v

Q: 12 above the Find the surface area of the portion of the plane 2r + 6y + 3z triangular region in the…

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Q: 7. Evaluate I = S ads, where S is the part of the plane x+y+z = a lying in the first octant.

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Q: Find the volum e the solid in The first octant in side The para boloid 2-22-y%=0 and below the…

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Q: Find the area of the surface of the part of the cylinder ? + 2² = 4 that lies above the square in…

A: For the given part of the cylinder  x2+z2 =4  which lies above the x-y plane at the vertices…

Q: 1. (1) In ry-plane, sketch the region R which is enclosed by the following: • the part of the circle…

A: The parameterization of line y=1 is x=t, y=1

Q: 63. Prove a famous result of Archimedes (generalizing Exercise 62): For r < s, the area of the…

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Q: 1. Find the volme of sold les between planes perpendicular to the x-axis at x = -1 and x = 1. The…

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Q: A. Find the area of the plane region bounded by the given curves 1. у%3Dх, у %3D 2х, and x + у %3D 6

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Q: 16. Parabolic cylinder cut by planes Integrate а. g(х, у, 2) yz b. g(x, y, г) %3D V4y² + 1 V4y² + 1…

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Q: he volumes of the solids generated by revolving the regions bounded by the graphs of the equations…

A: We have to find the volume about the given lines.

Q: O Find the area of the auface, using Polar oordinates, of the portion of the Cone x²+y² - 9z²=0…

A: Use polar coordinates x=rcos(theta) y=rsin(theta)

Q: What is the surface area of the portion of the surface z= x?+y that lays over the triangle on xy-…

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Q: find a parametrization of the surface. (There aremany correct ways to do these, so your answers may…

A: Given information: The surface equation of the cylinder is y2+z2=9 between the plane is x=0 and x=3.…

Q: Find parametrizations The portion of the sphere x2 + y2 + z2 = 36 between the planes z =-3 and z =…

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Q: 3) The base of the solid is the disk x2 + y2 s 9. The cross sections by planes perpendicular to the…

A: Let's find.

Q: (a) Show that the surface area of a zone of a sphere thatlies between two parallel planes is S = 2…

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Q: The trace of the surface S: z = a +y in the plane z = 4 is O a Line a Parabola O An ellipse O a…

A: Consider the given equation. S:z=x2+y2 and plane z=4 Put both the values equal. x2+y2=4

Q: a. Find a parametrization for the hyperboloid of one sheet x2 + y2 - z2 = 1 in terms of the angle u…

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Q: (a) Evaluate L(z+ 2y)dz + (x² – y²)dy where C is the line segment C1 from (0,0) to (1,0) followed by…

A: The line integral ∫CPdx+Qdy involves the integration over a specific path C. In this problem the…

Q: Find area the Surface generaled by revolving げ-28+1 1SI52 about y -akis

A: The area of a surface obtained by revolving a curve x=f(y) about the y axis is S=∫2π f(y)ds where…

Q: Use polar coordinates to evaluate S (5x-y) dA gion in the fourth quadrant bounded by the circles nd…

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Q: : The region D in the x, y plane defined by the inequalities 0 ≤ y ≤4, √√4y-1² ≤x≤ Isas √√16-₁², can…

A: We have use relation between cartesian and polar co ordinate system  x= r cosθ  , y = r sinθAlso…

Q: 5. Consider the surface obtained by rotating the graph of f(x) = 1/2, 221, around the z-axis. This…

A: We will show this using integration ∫1∞1xdx = ln x1∞ = limx→∞ln x = ∞

Q: 0lar coordinates to tind the volume: 2=6-R-y² and the paraboloid z=6-x-y² and 'ty² L4. 2. the plane…

A: For polar coordinates x^2+y^2 = r^2, dxdy = rdrdtheta x = rcostheta , y = rsintheta

Q: Find the centroids of region A and region B where region A is formed by an arc of a parabola that…

A: • First we need to find the area of the respective regions and then the moment of that area about x…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.