Let X = {1,2,3, 4, ...} and de fined metric on X as d (r, y) |r-yl %3D Find open ballB (2,2) = o {2} (0, 4) O {1.2,3} O 12.3] o {2,3}

Q: „Consider the space (R,T). where t={R,Ø}U{ACR:[0,1)CA} :Then (R,T) is not T, O T, but not T, O T2 O…

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Q: Let C be the positively oriented square with vertices (0,0), (1,0), (1, 1), (0, 1). Use Green's…

A: Let's solve by using green theorem.

Q: Let C be the positively oriented square with vertices 0, 1, 1 + i, i. Evaluate using the definition…

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Q: Let X (2,3. 4) and de fined metrie on X as d(x, y) = |-y Find open ball B (2.2) = (0) O (2) 0 2.0…

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Q: Suppose F(x, y) = (3x – 2y)i + 3xj and C is the counter-clockwise oriented sector of a circle…

A: Given, F→(x,y)=(3x-2y)i→+3xj→ Here, M=3x-2y and N=3x radius=3 θ=π3 Limits are 0≤r≤3 , 0≤θ≤π3

Q: Use Green's Theorem to evaluate the line integral. (a) | e2a+y dx +e¬Y dy, where C'is the triangle…

A: In the question we have to evaluate integral. NOTE - As per Bartleby's policy we can not solve…

Q: Write a homeomorphism between the unit closed disk A = {(r,y E R2 : a2 + y? < 1)} and the unit…

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Q: Consider the following mappings on RXR: d1(x,y) = e*-Y, d2(x,y) = |2x –yl and d3(x,y) V=yl O Both d1…

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Q: Let S be the sphere of radius 2 centered at (0, 0, 0). Let F(x, y, z) = . Show all supporting work.…

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Q: Verify Green's theorem for the disc D with center (0, 0) and radius R and the following functions.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

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Q: Calculate S," (2x+y) dV where V is a closed space bounded by the cylinder z = 4 – x2 and the planes…

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Q: Let B be the ball with center at the origin and radius 1 SS [3(x² + y² + z²)dV =

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Q: Let NR be a disc with centrum in origo and radius, R. 1 Assume that, J(x, y) x² + y? < R². 1+x2 + y²…

A: ΩR be a disk with centrum in origo and with radius, R. Assume that, Jx,y=11+x2+y2,x2+y2≤R2. Then we…

Q: Let d: Rx R*→[0, ∞) such that d(XF)=√(x, y)² show that (R.d) metric space.

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Q: Use Stokes's theorem to evaluate o F· dr, where F(x, y, 2) = xy² i+x²yj+yz k, where C is a…

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Q: Verify the Green's theorem for integral x²y dx + xy dy, where C is the boundary described…

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Q: View S' as the boundary of the 2-disk D² = {(x, y) E R² | x² + y? < 1}. Fix To E S', and let X = (S'…

A: Given : D2=x,y∈ℝ2|x2+y2≤1 where x0 belongs to S1 which the boundary of 2-disk. X=(S1×S1)∪(D2×x0) To…

Q: Use Green's Theorem to evaluate the line integral S(x² + y²)dx + (x² – y²) dy where C is the…

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Q: Exercise. a) For every ,r, y E R, let p(r, y) =| x² – y? |. Is pa metric U..... on R? b) For every…

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Q: If F = xy?i + yz? j + zx2k, and S is the region bounded by the triangle with vertices (1,0,0),…

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Q: Let C be the triangle with vertices (0,0), (2,0), (0,4) directed counter-clockwise, and let F(x, y)…

A: C be the triangle with vertices 0,0,(2,0), and 0,4. and F(x,y)=ey2+2x,4y+sin1+x3. we have to…

Q: Let X = R and x, y E R. Admit for all x and y the metric d(x, y) = |arctan x arctan y|. | Compare…

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Q: 4) Use Stokes theorem to evaluate SF.dr, where с F(x, y, z) = <.xy, yz, *x), where C is the triangle…

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Q: Compute the integral of the Gauß curvature over the surface shown in the picture. The three boundary…

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Q: Let C be the portion of the circle x² + y² = 4 from (2,0) to (0,2) traced counterclockwise. (a) (b)…

A: As per the question we are given a curve C which is a quarter circle defined as : x2 + y2 = 4  ,…

Q: Calculate ( (2x + y) dV , where V is a closed space bounded by the cylinder z = 4 – x? and the…

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Q: Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's…

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Q: The area bounded by the curve y = In(z) and the lines z = 1 and =2 above the z -azis is %3D square…

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Q: Verify Green's Theorem by evaluating both integrals aN aM dy dA ду ax for the given path. C: square…

A: Application of integration

Q: Prove that dr-V3Ta? where こis the intersection of the plates: x²+ and and F=ly,Z,x)

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Q: Evaluate x dV , where E is the E region in the first octant bounded by the sphere x² + y² + z² = 1…

A: given region is in the first octant. using spherical coordinates x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ and…

Q: If X =R and d(x,y)= 1, then X not metric semi metric metric space

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Q: Let W be the region that is cut aut from x't v<4 by the pora blae id Rs X'ty ond the plane =10.…

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Q: Let d(x,y) = |1/x - 1/yl be a metric on RI(0}XRI(O}. Then the open ball of center 1/2 and radius 1/3…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: Use Green's Theorem to evaluate x dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: Use Green's theorem to calculate the work done by force F on a particle that is moving…

A: GivenF(x,y)=x32-8yi+5x+8yj,C: Boundary of a triangle with vertices (0,0), (5,0) and (0,5)To…

Q: A solid G is bounded by the paraboloid z = 4 – r - y², the cylinder 2+ y = 4 and the plane z = 5.…

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Q: Use Green's theorem to compute the circulation of F(x, y) = (-y, x²) around the perimeter of the…

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Q: Let d : R x R → R be defined to be d(x, y) = | arctan(x) – arctan(y)|. Show that d is a metric on R.

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Q: Verify that (S, d) is a metric space. 10.2 Prove that d(x, y) < d'(x, y)s/2 d(x, y) for all points'…

A: To prove dx,y≤d'x,y≤2dx,y for all points x,y∈ℝ×ℝ where d is the usual metric and d' is the…

Q: Let S be part of the outward-oriented hyperboloid of one sheet x² + y² = z² = 1 that lies within the…

A: Given x2+y2-z2=1 and x2+y2+z2=3

Q: . Let F(x, y, z) = (x³, y³, z³). Use Gauss's theorem to find ffsF dS if S is the sphere x? + y? + 22…

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Q: 4. Find the curvature of r(t) = (tv2, e', e-t) at the point (0,1,1).

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Q: Let d(x.y) = |1/x - 1/y be a metric on R(0)XR\(0). Then the open ball of center 1 and radius 1/4 is*…

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Q: verify Stokes § = (a%-y)i - yz'i over the uppea hazf SOD Face Of the sphere =1 bounded by the

A: Given that,  F→=(2x-y)i→-yz2j→-y2zk→ To verify Stoke's theorem: ∫CF→·dr→=∬Scurl F→·n^dS Here C is…

Q: Let X = R², x, y EX where x = (x₁, x2), y = (y₁.Y2) with the metric function (4 pts) (x, y) =…

A: This is a question of topology and metric space.

Q: Let X=ℝ2 and define d2,:ℝ2×ℝ2→ℝ by d2((x1 ,y1),(x2,y2)) = max{|x1 - x2|,|y1 - y2|}. a) Verify that…

A: Given that X=ℝ2 and defined by d2:ℝ2×ℝ2→ℝ Part(a): Now from given d2:ℝ2×ℝ2→ℝ by…

Q: Let X = {2,3, 4,..} and de fined metric on X as d (r, y) = |- yl %3D %3D Find орen ball B (2,2) =…

A: Follow the definition: B(2,2) = { x in X : d(x,2) &lt; 2 }

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.