2) Let X- {а, b, с, d} T-{X, о, {a}, {b}, {а, b}}. Computethe closure, interior and boundary of A in each of the following cases:(i) A= {a}||(ii) A= {b}( iii) A= {d}.

Here given set X=a, b, c, d and the topology on set X is given as I=X, ϕ, a, b, a, b

Answered: 2) Let X= {a, b, c, d} J= {X,Ø, {a},…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. A robot performs the following operations on a set of points (x,y) in the 2D plane to check the movement of objects where (x,y) E Zxz (a, b)A(c,d) = (c + a. 2db) Algebraic characteristics of the Summarize and Find the Abstract operation above.
2. Let a,, az,., a, be numbers. Show that there is a single number r such that foo: (z-a) +(2 – a,)° +..+ (x – a,) is a minimum and find this number.
4 Let y = 9 u1 U2 and W = Span (u1,u2). Complete parts (a) and (b). a. Let U= u, u, . Compute UTU and UUT. UTU=D and UUT = (Simplify your answers.)
3. Express the following regions in the stated coordinate systems. You do not need to justify your answer but showing your though process may help with partial marks. Your answer should be a set in the following form: {(V1, V2, V3) : a ≤ v₁ ≤ b, f(v1) ≤ v2 ≤ g(v1), Ø(V1, V2) ≤ v3 ≤ (v₁, v₂)} where (v₁, V2, V3) are the three variables of the coordinate system in questions in any order, a, b R are constants, f, g are functions of v₁ and 6, are functions of v₁, V2. (a) The region outside the cylinder x² + y² ≤ r² and inside the sphere x² + y² + z² r< R. Express this in the cylindrical and spherical coordinate systems. - R² assuming (b) The region in the first octant (x, y, z ≥ 0) below the plane x + 2y + 3z = 6. Express this in the cylindrical, spherical and Cartesian coordinate system.
b) Compute f. F. dr where c is the boundary of the square [0, 1] × [0, 1] where F = (–y², x²).
Q5. Let A(0,0), B(2,0), C(1,1) be points in the plane R.Then the following is not a convex set: A)The Triangle ABC B)[2,4)x(0) C) [2,4]x(3) D) (2,-)x (,0) DC

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2) Let X= {a, b, c, d} J= {X,Ø, {a}, {b}, {a, b}}. Compute the closure, interior and boundary of A in each of the following cases: (i) A= {a} (ii) A= {b} ( iii) A= {d}.