QI: Let (M, d) be a metric space and S,T C M. Then 3NT = SNT if (a) SST. (b) TCS. (e) S=T. (d) All the previous. (a) O (b) (c) (d) O
Q: 19. f(x, y) = x + y+y+ 1, constrained to the triangle with vertices (0, 1), (-1,–1) and (1, +1). %3D
A: As per bartleby guidelines i can answer only one question, kinldy upload rest questions separately.…
Q: Let d: R? x R² →R, defined as d (x, y) = |x1 - yı|+ |#2 – y2]| where x = (x1, x2), y = (y1, y2) ,…
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Q: Sketch the space curve. Function r(t) = -ti + 2tj + 4tk -2 -2 OY 10 Z Z 2 2 5 5 Find its length over…
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Q: Use Stoke's Theorem to evaluate Į F· dr where F (x, y, =) = , and C is the triangle with C vertices…
A: given Fx,y,z=z2,y2,xy ⇒Fx,y,z=z2i^+y2j^+xyk^ and a traingle C with vertices 1,0,0 ,0,1,0 ,0,0,2 to…
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A: Consider the given identity of parallelogram law on inner product space. Using distributive law…
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A: Given function is f(x,y)= e^-2y cos2x
Q: (c) Use Green's Theorem to evaluate (3xydx+ 2xy dy, where C is a counterclockwise oriented…
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Q: Let (x, y) and (z, w) be two points in R? state which of the following does not define metric on R?…
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Q: The Minkowski metric of special relativity is ds? = -dt? + da² + dy? + dz². Express the metric and…
A: Answer is mentioned below
Q: Find T, N, and x for the space curve r(t) =7i+j,t>0. T(t) = (O i+ (O i
A: Formula for T, N and k are defined as T=vv, where v=drdt N=dTdtdTdt and k=1vdTdt
Q: 1. Determine which of the following function define a metric on R : (i) d(r, y) = V ly° + |x|° (ii)…
A: Metric: A metric, d on X is a function defined on X × X such that for all x, y, z ∈ X, which…
Q: Use Stoke's Theorem to evaluate $. F · dR, where F (x, y, z) = (z²,xy, xz) and C is the triangle in…
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Q: Find T, N, and k for the space curves r(t) = (cosh t)i - (sinh t)j + tk
A: Let the given space curve is r(t)=(cosh t)i-(sinh t)j+tk To determine: The values of the unit…
Q: Identify the theorem: If S is the boundary surface of a solid E in 3-dimensional space, then SS, F.…
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Q: a) Rewrite the expression P= f(Q, D, 52, P,H) in dimensionless form by using Pi- theorem, where P is…
A: image is attached
Q: (b) The Minkowski metric of special relativity is ds? = -dt? + dx? + dy? + dz?. Express the metric…
A: First, determine the derivative of x' and y' and other variables too. Now determine the metric of…
Q: The movement of a particle follows g(u), where g(u) h(u) and h(u) = u? + 8u + 15 and y(u) = u² + 2u…
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Q: Use Stokes's Theorem to evaluate JeF - dr- . In each case, C is oriented counterclockwise as viewed…
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Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.
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Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw
A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv , y=3uv-uvw and…
Q: Find T, N, and K for the space curve r(t) = (9 sin t) i + (9 cos t) j+ 12t k. T(t) = (O i+ O i+ (O k
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Q: Find the expression of the metric ds? = (dx')? + (dx²)² + (dx³)² and it's 1st and 2nd components of…
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Q: d: R? x R? -R Q2: Let d(a, b) = |b, - al+ do(a2 ,b2), where do denotes the discrete metric on R.…
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Q: (ii) Use the rescalings s = S/N, i = I/N, t = BN1, c = µ/(BN) and d = y/(BN) to non-dimensionalise…
A: differential equation representing disease with classes S , I , R dSdt=-βSI+γRdIdt=βSI-μIdRdt=μI-γR…
Q: P2(x, y) = (E | x; – Yi [°)} i=1 s metric forms a metric space on ( ?
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Q: Let (x, y) and (z, w) be two points in R? state which of the following does not define metric on R?…
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Q: hy sphere x + y +z = 25 between planes z=2 and z= 4.
A: We need to find surface area using double intergral.
Q: Transform pentagon BEARS according to (xy) → (x + 6, y+8). Write the coordinates for pentagon…
A: Given Data: Traformation: x, y→x+6, y+8 The given figure in the problem represents the pentagon…
Q: (b) Let X = {r € R: -1 <1<0or 0 <1< 1} with the usual metric.Then X is disconnected.
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Q: (10) Define the metric d on R² by d( (x₁, y₁), (x2, y2)) = max{ |x₁ − x2\,|y₁ - y2|}. Verify that…
A: The given problem is to verify that the given metric d on R2. Given metric…
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: erify The Divergence Theorem. F(x, y, z) = (x – 2)i + (y – x)ĵ + (z – y)k is the cylinder æ² + y² =…
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Q: Transform pentagon BEARS according to (x, y) → (x +6,y+B). Write the coordinates for pentagon…
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Q: Use the Divergence Theorem to evaluate F. dS , where F(r, y, z) = (2x(y - z), x? – y, z) and S is…
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Q: dA, where K is the disk r + (y 2 +?
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Q: Exercise 11. iz Let f(z) and CR be the upper half circle with center (0,0) and radius R z5+1 taken…
A: Option (a) is correct.
Q: JJs where S is the sphere x² + y2 + z2 = 1.
A: Given S is the sphere x2+y2+z2=1 To evaluate: ∫∫S3x+3y+z2dS…
Q: 8. f(x, y) = R is the disk x +y < 9. %3D x² + y? + 1' 1. 1.
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Q: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.
A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9
Q: Ix-yl 1 + |x-yl ₁ = R₁ d (x,y) = R is matric space
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Q: Consider the solid in xyz-space, which contains all points (x, y, z) whose z-coordinate satisfies 0…
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Q: A) Find B and t for the space curve r(t): = (3 sin t)i + (3 cos t)j + (t)k.
A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question…
Q: 8 Find T, N, and k for the space curve r(t) = Gi+gj, t> 0 8
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Q: Find T, N, and k for the space curve r(t) =i+ i, t>0_
A: In this question, we find the unit tangent and unit normal along with the curvature of given r(t)
Q: B) Use Green's Theorem to evaluate F-dr, where C is the triangle with vertices (0, 0) (3,0) and (3,…
A: Explained below
Q: Prove the parallelogram law on an inner product space V; that is, show that ||x+y||² + ||x-y||² =…
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Q: Q. FOR THE SPACE VECTORS SHOWN BELOW FINDS ( , 1, , B, p,ANDT).1- FOR GROUP A AND 2- FOR GROUP B.…
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Q: d(r, y) 1+d(x,y) 5. Let (X, d) be a metric space. Define f : X x X → R by f(r, y) = Show that f is a…
A: (χ , d) be a metric space , define f :χ×χ→ℝ by f(x , y)=d(x , y)1+d(x , y) Positive definite…
Q: Find T, N, and K for the space curves in r(t) = (t^3/3)i + (t^2/2)j, t> 0
A: Given: rt=t33i+t22j
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- 1. a) Let (x, d) be a metric space. Define a flow on (x, d). b) Let (x, {ϕt}) be a flow on a metric space X. When is xo in x a fixed point of the flow? c) When do you say that a fixed point xo in x is Poincare stable? d) When do you say that a fixed point xo is Lypanov stable?A. Let H be the set of all points (x, y) in ℝ2 such that x2 + 3y2 = 12. Show that H is a closed subset of ℝ2 (considered with the Euclidean metric). Is H bounded?Is the set S = [0,1] with the discrete metric d separable? Explain.
- the usual metric space defined by d(x,y)= x-y prove the four propertis of metric space1. a) Let (x, d) be a metric space. Define a flow on (x, d). b) Let (x, {phi_t}) be a flow on a metric space x. what is x0 in x a fixed point of the flow? c) When do you say that a fixed point x0 in x is Poincare stable? d) When do you say that a fixed point x0 is Lyapunov stable? Use Analysis to complete the following statements.Consider the following geometry problems in 3-spaceEnter T or F depending on whether the statement is true or false. 1. Two lines either intersect or are parallel 2. A plane and a line either intersect or are parallel 3. Two planes orthogonal to a third plane are parallel 4. Two lines orthogonal to a third line are parallel 5. Two planes parallel to a line are parallel 6. Two lines parallel to a third line are parallel 7. Two lines parallel to a plane are parallel 8. Two lines orthogonal to a plane are parallel 9. Two planes orthogonal to a line are parallel 10. Two planes either intersect or are parallel 11. Two planes parallel to a third plane are parallel
- Prove that topological space E is not homeomorphic to the spaceY = {(x, y) ∈ E^2 : y = ± x} (E represents R equipped with Euclidean distance, E^2 represents R^2 equipped with euclidean distance)2.) Let (S, d) be a metric space and suppose that ρ : S × S → R is defined byρ(x, y) = d(x, y)1 + d(x, y)for all points x, y ∈ S. Prove that (S, ρ) is a metric space, that it is bounded and thatρ(x, y) ≤ d(x, y) for all x, y ∈ S.Show that ℓ^1 is a normed linear space.
- A. Let H be the set of all points (x, y) in ℝ2 such that x2 + xy + 3y2 = 3. Show that H is a closed subset of ℝ2 (considered with the Euclidean metric). Is H bounded?A. Let H be the set of all points (x, y) in ℝ2 such that x2 + xy + 3y2 = 3. Show that H is a closed subset of ℝ2 (considered with the Euclidean metric). Is H bounded?Give the set of limit points A0 of a singleton A = {(5, 2)} on the plane R2 with the discretemetric.Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are homotopy equivalent. (E^2 represents R^2 equipped with euclidean topology)