Exercise.3 Show that the following the functions d and p on X = R? are metrics or not, such that 2. d((x1, x2), (Y1, y2)) = max{Ix1 - yıl. x2 - yal}

Q: Does the following function satisfies the symmetry condition? a(v, u) = f(vxK Ux +vAu)dx -1

A: Given,        a(v, u)=∫-11(vxκux+vλu)dx

Q: QUESTION 8 The set M with the usual metric is connected. 2 O True O False

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: and f, and evaluate each at the given point. A(x, Y) = arctan(), (6, -6) %3D fx(x, y) = %3D fy(x, y)…

A: fx, y=arctanyx6, -6To find fx and fy

Q: (2) In R with the usual metric. Let A = (1, 3]u{4}, find: A°, A', A, g.l.b(A) and 1.u.b(A).

A:

Q: ?, R(A)IN(A*)

A:

Q: 5) Let à = psin(4)ū, + p² Ug Evaluate f Ã. dl given that L is the contour of the following figure.

A: Let A→=ρsinϕu→ρ+ρ2u→ϕ we have to evaluate ∮A→.dl→

Q: 6. If Z is the ocentroid of AWXY, WR = 87, SY = 39, and YT 48, find each missing measure. W a) WS =…

A:

Q: 5. Let d be a metric on X. Determine all constants k such that (i) kd, (ii) d+ k is a metric on X.

A: Given that d be a metric on X. Then d:X×X→[0,∞) satisfies the following conditions for x,y,z∈X, (a)…

Q: 2) Determine the dimension of Null A and Col A for the marix 1 2 30 0] A =0 0 1 0 1 0 0 0 1 0

A:

Q: Define p: R^2 x R^2 to [0, infinity) by the rule p(x1,y1),(x2,y2)=squareroot((x1-x2)^2+(y1-y2)^2)…

A:

Q: Consider the following mappings on RXR: * d1(x,y) = ex-y, d2(x,y) = |2x -y and d3(x,y) = √√x - yl O…

A: The given problem is to check which mappings are metric in R. We have to check metric properties of…

Q: QUESTION 5 The set R-{0} with the usual metric is connected. O True O False

A:

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: I Find for each of the following. keving your anwer in terms of the parameter . 2r, y- 2

A: We have to find dydx for the following...

Q: Let M = 0,2) and d be the usunl metric, then dis not complete O True O False

A: False

Q: In which of the following cases is the mapping x: R² → R³a patch? (а) x(и, v) — (и, uv, v). (c) x(и,…

A: A mapping defined from x : R3 to R2 is defined a patch if x maps U diffeomorphic ally onto x (U) As…

Q: QUESTION 8 The set M={XEN:x<} with the usual metric is connected. O True O False

A:

Q: (2) In R with the usual metric. Let A (1,3] U {4}, find: A°, A', A, g.l.b(A) and l.u.b(A).

A:

Q: - Show that the area of the triangle whose vertices are the [x1 yi det X2 Y2 A - points (x₁, y₁),…

A:

Q: Find f and f, and evaluate each at the given point y' f(x, у) arctan (2, -2) fx(x, y) = %3D fy(x, y)…

A: The  given function is f(x,y)=arctanyx,      arctanyx=tan-1yx and the point is 2, -2. Now we have to…

Q: 12) Find the clamped cubic spline for the data (1,1),(3,4), using that f'(1) = 2, f'(3) = 5

A:

Q: Find f, and f, and evaluate each at the given point. y' f(x, y) = e*y2, (In 4, 2) f,(x, y) = %3!…

A: We can find the answer as below,.

Q: (2) In R with the usual metric. Let A = (1,3] U{4}, find: A°, A', A, g.l.b(A) and l.u.b(A).

A:

Q: A function e : X → Y is an embedding if one ond for V

A:

Q: If C is the circle |z|=4 evaluate Sf(z)dz for each of the following functions using residue. (a)f(2)…

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

Q: 2. Let d1, d2 be two metrics on X + 6. Show that: d(r, y) = d1(x, y) + d2(x, y).

A: I have proved all four conditions of metric for d

Q: graph the points z = x + iy that satisfy the given conditions. 5. |z + 1| = 1 6. |z + i |= |z - 1|

A: Hi there, at a time we can answer only one question at a time and the exact one was not specified.…

Q: 1. Let (S, d) be a discrete metric space and p e S. Identify S (p), S1 (p), S2(p). 2. Let R have the…

A: We are entitled to solve only one question at a time. As the question number is not mentioned, so we…

Q: 2.1.12. Determine which of the following is a metric on R. (a) d(x, y) = x – y. (b) d(r, y) = (x –…

A:

Q: QUESTION 8 The set M= EN: X< with the usual metric is connected. O True O False

A: Since you have asked more than one question. So we will solve first one for you. If you want other…

Q: QUESTION 16 The set S=fxER:x² -4<0} with the usual metric is O A. Compact. O B. connected. OC Not…

A:

Q: Define new metric which is different from giving in above questions on X in question 01.

A: With the help of questions 01 we define a new metric on X

Q: Consider the following mappings on RXR: * d1(x, y) = e2z-y, d2 = |2x – 2y|, and d3 = VI2x – y|. %3D…

A:

Q: 1. Prove that given a line € and a point P not on e, there exists a line through P perpendicular to…

A: Explanation of the answer is as follows

Q: Eliminate Band a for the relation. x=Bcos(wt+a) in which w is a parameter. *

A:

Q: QUESTION 5 The set R/{O1 with the usual metric is not connected. O True O False

A: 5. TRUE The set, R - {0} with the usual metric can be written as the disjoint union of, (-infinity,…

Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

A:

Q: . Let X be a nonempty set with metric d. Show that the function e defined by e(x, y) = min[1, d(x,…

A: We know that d(x,y) is a metric on X. Hence d satisfies all the properties of a metric.  Now e(x,y)…

Q: Let X = R? , and let d2 be the usual, Euclidean metric on X. Define another metric, d : X x X → R,…

A:

Q: 6. The distance between a point x ER and a nonempty set A CR is defined by d(x, A) = inf {\x – y| :…

A: In this question, we have to prove that d(x,A)=0 iff x belong in closer(A)

Q: Define a metric as d(x,y)=|x1-y1|+|x2-y2|. Find the set of all points x=(x1,x2) in R2 such that…

A:

Q: Let X= {3,4,5,....} and A={4,6} and metric defined on X as d(x,y) |= |x - y Find interior of A (1)…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: 9 on X= IR, k>o. Define metrics ond q P is not in the form kq for

A:

Q: Given an example of a linear map T: R4 → Rª such that range T = null T (or equivalently range T =…

A:

Q: Consider the following mappings on RXR: d1(r, y) = e , d2 = |2.r – 2y|l. and d3 = v2r - yl. None of…

A:

Q: Let S=25| be subset of R.Which of the following statements is true? Select one: O A. Sis linearly…

A:

Q: Let X = {a, b, c} Define d: X2[0, 0) by d(a, a) = 0, d(b, b) = 0, d(c, c) = 0, d(a, b) = 1, d(a, c)…

A: Metric Space: Let X be a set and a function d :X×X→ℝ Then X, d is a metric space if d satisfies the…

Q: ■ Show that the area of the triangle whose vertices are the [X1 У1 points (x₁, y₁), (X2, Y2) &(X3,…

A:

Q: Find f and f, and evaluate each at the given point. y' f(x, y) = e*y, (In 4, 2) f,(x, y) = f,x, y) =…

A:

Q: Let X=R2 and let d be the Euclidean metric.  Define d3:  R2 x R2 to R by d3(x, y) = min{1, d(x, y)}…

A: Euclidean metric: The Euclidean metric d on ℝ2 is defined as follows: dx1, x2, y1, y2=x1-y12+x2-y22…