Sketch the region in the z-plane represented by the following set of points: |z+i|+|z-i|≤3

Q: Find the area of the plane region bounded by y=-x+2 and y=x²-2x 07 s.u. 9 9 s.u. 01 S.U. 2 S.U.

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Q: sketch the region described by the followingspherical coordinates in three-dimensional space. 0 ≤ρ ≤…

A: Given: The region bounded by 0 ≤ρ ≤ 1, π/2 ≤ f ≤ π, 0 ≤ θ ≤ π.

Q: Evaluate ſf, (3x + 4y²) dA where R is the region in the upper half - plane bounded by the circles x²…

A: As the areas are circular thus convert the integral into polar form. Now determine the limits of the…

Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

A: 25.   Given that:   The plane y+z=2 and the cylinder x=4-y^2. The region in the first octant bounded…

Q: Evaluate fxz ds, S is the boundary of the region enclosed by the cylinder, y² + z² = 9 and the…

A: We have to evaluate the integral ∫SxzdS, where S is the boundary of the region enclosed by the…

Q: Verify: Green's theorem in the plane for f(2x-y³) dx-xydy, where C is the boundary of the region…

A: Given information ∫c2x-y3dx-xydy Here, C is the boundary of the region enclosed by the circle…

Q: Let R be the region in the plane enclose

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Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

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Q: Consider a region R, which lies above the x-axis and between the circles x² + y? = and x? + y? = n²…

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Q: Let R be a region bounded by the four planes x = 0, y= 0, z= 0 and x + y + z = 3. Evaluate SS 24x dV…

A: we have to evaluate the following integral

Q: Evaluate fR z = Jx2 + y2 x2 + y2 + z2dxdydz, where r is the region bounded by the plane z = 3 and…

A: We will convert integral into spherical co ordinate system . 1st relation between cartesian and…

Q: Let R be a region bounded by the curves y = x² and y = 4x – x². Evalua /| (a + y)dA. R

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Q: Evaluate || xdA, where R is the finite region bounded by the axes and 2y +x = 2. R

A: Given: I=∫∫RxdA And 2y+x=2⇒y=1-x2 We know that; ∬dA=∬dydx or ∬dxdy   Now find the x & y…

Q: Given that C is the boundary of a region bounded by y=-9+x', y =x-3, x 2 and y = 0 with positive…

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Q: Determine the surface area of f(x,y) = 2+ (2/3)x^(3/2) + (2/3)y^(3/2) over the region R, a triangle…

A: If we look x varies from 0 to 2  y varies from 0 to 2

Q: Let M be the region bounded by the parabola y = r² and the line y = x + 2. %3D 6. y = r +2 5. 2,4)…

A: Given that, The shaded region bounded by the parabola y=x2 and the line y=x+2 is M.   And the region…

Q: Let R be the region consisting of the points (x, y) of the Cartesian plane satisfying both ∣x∣ − ∣y∣…

A: Let R be the region consisting of the points (x,y) of the Cartesian plane satisfying both…

Q: Let R be the annular region lying between the two circles x² + y² = 1 and x² + y² = 9. Evaluate the…

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Q: Given that C is the boundary of a region bounded by y =-9+x, y = x-3, x= 2 and y = 0 with positive…

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Q: Consider the following. y = Vx - 2) (x - 8)2 y = 0 X = 2 X = 8 (a) Use a graphing utility to graph…

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Q: Use the Trapezoidal Rule to estimate the number of square meters of land, where x and y are measured…

A: The formula for Trapezoid rule is h2y0+yn+2y1+y2+y3+..... where h=b-an

Q: Let R be the region bounded by the graphs of y = x +3, y= x³ +1 and the lines x = 1 and y = 0 as…

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Q: Let D be the region in xy-plane enclosed by the Trapezoid with vertices at the points (1, 1) , (7 ,…

A: We need to use double integral across given trapezium

Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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Q: Let R be a region bounded by the four planes a = 0, y = 0, z = 0 and r + y + z = 4. Evaluate SSS 24x…

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Q: Find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes and…

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Q: Let R be a region bounded by the four planes a = 0, y = 0, z = 0 and a + y + z = 9. Evaluate SSS 24x…

A: In this question we will use basic of calculus i.e application of integration. We will simply apply…

Q: 7) Verify Stoke's theorem when F= (2ry- a)î – (x² – y²)ĵ and C is the boundary of region enclosed by…

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Q: Evaluate SSS z²dV, where R is the region given. R by above the plane Z=0 and between the sphenes + 2…

A: In spherical coordinates,                                             So,

Q: / y cos(r*)dA. R

A: Given:- Let R be the region in R2 bounded by the x-axis, the parabola y = x2 and the line x = 2

Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: Find the surface area of the piecewise smooth surface that is the boundary of the region enclosed by…

A: Consider the given function. z=7−5x2−5y2 and z=2x2+2y2 Put the both function equal.…

Q: Sketch the region in the z-plane repres ented by the following set of points: (i) Iz +il+ |z - il 3.…

A: .

Q: Let R be the region bounded by the graphs of y = VT, y = e, and the y-axis.

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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: Consider the plane region bounded by the graphs of y = k, y = 0, x = 0, and x = b, where k > 0…

A: Given: The plane region is bounded by the graphs given as follows, The plane is drawn for the given…

Q: If R is the region enclosed by a simple closed positively-oriented curve C, then the area of R is…

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Q: Find the volume of the Intersection curve C C Projection of C on ay-plane

A: Given: Given paraboloids are z=x2+y2 and z=8-x2-y2 We want to find the volume bounded by the…

Q: Let R be a region bounded by the curves y = x2 and y = 4x – x2. Evaluate | (x+ y)dA. 2.

A: When a function of two variables is integrated over a region, the double integral is used. It is one…

Q: 2. Sketch the two dimensional planar region R = {(x, y) | 0 <x < 2, x² < y < 2x}.

A: Solution Given Seetch the two dimensional planar region R={(x,y)|0≤x≤2,x2≤y2x}

Q: Let R be a region bounded by the curves y = r and y = 4x – x². Evaluate (r+ y)dA.

A: Given: I=∫∫Rx+ydA And y=x2 ; y=4x-x2 Now find the point of intersection between the curves;…

Q: Show that Green's theorem is satisfied for R as the positive boundary of the region shown in the…

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Q: Let R be a region bounded by the four planes x = 0, y 0. z O and r + y + z = 11. Evaluate LIS 24x dV…

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Q: /| f(r,y) dA = f(r, y) drdy + /. II F(7,y) dzdy

A: Solution:

Q: Show that the mapping w = (1 – j)z, where w = u + jv and z = x + jy, maps the region y > 1 in the z…

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Q: Let M be the region bounded by the parabola y = x² and the line y = x +2. %3D 6. y = r + 2 5. 4.…

A: Consider the given information and diagram: Let y=x2 and the line is y=x+2.

Q: Find the area of the surface. The part of the plane 3x + 5y + z = 15 that lies in the first octant

A: Given plane,  3x+5y+z=15Intercepts of the plane axis are  x=5, y=3, z=15

Q: Let D be the region bounded by (a) y = (0 < a< 1),

A: As many parts and its further sub parts are given, so I will solve only one ( Question (a) and its…

Q: Find the area of the finite part of the paraboloid  y = x2 + z2 cut off by the plane y = 4.

A: To find the area of the finite paraboloid y=x2+z2 cutt off by the plane

Q: Evaluate drdy over the region R which is enclosed by the lines r+ y = ±1 r + y + 2, and r – y = ±1

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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.