showthat two metricspace s (Xyd) and (X,d) are home omorphicifand onlyifevery open battin(Xd)contains as open ball centered at the sam e pointin Exd) and con versely

Q: which of the toihts PC6,L3), Q (-5,-1,4), and R(0,3,8)15 c losest to the X2-Plane? which paint lies…

A: A point in 3D has (x,y,z) coordinates. A point on XY plane has (x,y,0) coordinates i.e. z=0 A point…

Q: Draw the Taxi-metric hyperboloid |x| + |y| + |z| = 1

A: As per the question we are given the equation of Taxi-metric hyperboloid as : |x| + |y| + |z| = 1…

Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a1,…

A:

Q: Let X = (1, 2, 3), Tx = (0, X, (1), (2, 3}}, then (X, Tx) is %3D %3D 1) a T1 space 2) a T2 space

A: T1 space: A topological space X has the T1 property if x and y are distinct points of X, there…

Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: Let y= - Find the intersection of these surfaces, Calculate the GB of wrt lex order x>4>2)

A:

Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

Q: Give an example of (v1, v2, v3) and (w1, w2, w3) independent se- quences in the R“ such that…

A:

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: Give an example of (v1, v2, v3) and (w1,w2, w3) independent se- quences in the Rº such that…

A:

Q: (b) Every continuous map S? →T² is homotopic to the constant map.

A:

Q: Which of the following are suspaces of 1 2 1 R4 whereu , v = 1 -1] Select one or more: A. {w; w. v =…

A:

Q: (d) Let (Fn) be a sequence of closed subsets of M, and S, (j = 1,...,5) be subsets of M such that.…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 2. Do the three planes X + 2y + z = 4, y - z = 1, x+ 3y = 0 have at least one commom point of…

A: The equation of the plane is given by the formula ax+by+cz+d=0. The system of planes can be solved…

Q: Fud the Line pussing through the posnt (!,-l,o) and purrllel to the Eme of intersection of planes (X…

A:

Q: (4) 2 What is the square of the (minimum) distance between W and P? Let W Span< = -2 be a plane in…

A: Given that

Q: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

Q: Use Lagrange multipliers to find all points on the cone z2 = x² + y² that are closest to the point…

A: The solution has been given below.

Q: Sketch the following sets of points in the x-y plane. {(x, x^2): x is in R}

A: