according to the definition of type 1, 2, 3 on the first image, could u please explain the question on image2 specifically? thanks! Definition: Let 1: [a, b] → R and 2: [a, b] →R be continuous functions satisfying 2(t) ≤ 01(t)for all t€ [a, b]. Let R = {(x, y) : x € [a, b], y € [02(x), 01(x)]}. Then R is a region of type 1.Definition: Let 3 : [c, d] → R and 4: [c, d]for all te [c, d]. Let S=R be continuous functions satisfying 04 (t) ≤ 03 (t){(x, y): y = [c, d], x = [04(y), 03(y)]}. Then S is a region of type 2.Definition: A regionof type 3 is one that is both type 1 and type 2. 2. Sketch the following subsets of R2 and decide whether they are of type 1 (only), type 2 (only), type 3(both), or neither, justifying your answer.(a) A circle centred at (5,5) with radius 4.(b) The set of points (x,y) such that 0≤x≤5 and y ≥ 0.(c) The set of points (x, y) such that -1 ≤x≤ 1 and 0 ≤ y ≤ 1.(d) The set of points (x, y) such that 0 ≤ x ≤1 and x³ ≤ y ≤√√x.

Type 1 : A Type 1 region lies between two vertical lines and the graphs of two functions of x.Type 2…

. Sketch the following subsets of R2 and decide whether they are of type 1 (only), type 2 (only), type 3 both), or neither, justifying your answer. a) A circle centred at (5,5) with radius 4. b) The set of points (x, y) such that 0≤ x ≤ 5 and y ≥ 0. c) The set of points (x, y) such that -1≤ x ≤1 and 0 ≤ y| ≤ 1. d) The set of points (x, y) such that 0 ≤ x ≤ 1 and x³ ≤ y ≤ √x.

. Sketch the following subsets of R2 and decide whether they are of type 1 (only), type 2 (only), type 3 both), or neither, justifying your answer. a) A circle centred at (5,5) with radius 4. b) The set of points (x, y) such that 0≤ x ≤ 5 and y ≥ 0. c) The set of points (x, y) such that -1≤ x ≤1 and 0 ≤ y| ≤ 1. d) The set of points (x, y) such that 0 ≤ x ≤ 1 and x³ ≤ y ≤ √x.

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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Question

according to the definition of type 1, 2, 3 on the first image, could u please explain the question on image2 specifically? thanks!

Definition: Let 1: [a, b] → R and 2: [a, b] →R be continuous functions satisfying 2(t) ≤ 01(t)
for all t€ [a, b]. Let R = {(x, y) : x € [a, b], y € [02(x), 01(x)]}. Then R is a region of type 1.
Definition: Let 3 : [c, d] → R and 4: [c, d]
for all te [c, d]. Let S
=
R be continuous functions satisfying 04 (t) ≤ 03 (t)
{(x, y): y = [c, d], x = [04(y), 03(y)]}. Then S is a region of type 2.
Definition: A region
of type 3 is one that is both type 1 and type 2.

2. Sketch the following subsets of R2 and decide whether they are of type 1 (only), type 2 (only), type 3
(both), or neither, justifying your answer.
(a) A circle centred at (5,5) with radius 4.
(b) The set of points (x,y) such that 0≤x≤5 and y ≥ 0.
(c) The set of points (x, y) such that -1 ≤x≤ 1 and 0 ≤ y ≤ 1.
(d) The set of points (x, y) such that 0 ≤ x ≤1 and x³ ≤ y ≤√√x.

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