. 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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
icon
Related questions
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.
Transcribed Image Text: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.
Transcribed Image Text: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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 3 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage