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1. Draw the region Ni = {(x, y) : 0

1. Draw the region Ni = {(x, y) : 0

Advanced Engineering Mathematics
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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Numeracy 4. Some regions N in R2 can be written down by describing the functions which form their boundaries. For example, the set 2 = {(x, y) : -1 <x < 2, –1 – x <y <1 - x2} is drawn below: y = 1– x2 y = -1 - x Hence, if a 1 (as shown in the diagram) then the set describes all possible y-values between -1-a = -1-(1) = -2 and 1 - 22 =1-(1)2 = 0. 1. Draw the region N1 = {(x, y) : 0 <x <1:1-x < y < 2 - (x – 1)2} U{(x, y) : 1< x < 2 : x – 1<y < 2 - (x – 1)2} No explanation is required. 2. Let N2 be the region bounded by the curves y = x|x| and y = x. Write this region in the form N2 = {(x, y) : a <x <b: f(x) < y < 9(x)} for some choice of functions f and g. Note: You may need to break your region into multiple parts and take unions. 3. Let N2 be the same region as in part (2). Write this region in the form N2 = {(x, y) : c Sysd:a(y) < a< B(y)} for some choice of functions a and B. Note: You may need to break your region into multiple parts and take unions.
Transcribed Image Text:Numeracy 4. Some regions N in R2 can be written down by describing the functions which form their boundaries. For example, the set 2 = {(x, y) : -1 <x < 2, –1 – x <y <1 - x2} is drawn below: y = 1– x2 y = -1 - x Hence, if a 1 (as shown in the diagram) then the set describes all possible y-values between -1-a = -1-(1) = -2 and 1 - 22 =1-(1)2 = 0. 1. Draw the region N1 = {(x, y) : 0 <x <1:1-x < y < 2 - (x – 1)2} U{(x, y) : 1< x < 2 : x – 1<y < 2 - (x – 1)2} No explanation is required. 2. Let N2 be the region bounded by the curves y = x|x| and y = x. Write this region in the form N2 = {(x, y) : a <x <b: f(x) < y < 9(x)} for some choice of functions f and g. Note: You may need to break your region into multiple parts and take unions. 3. Let N2 be the same region as in part (2). Write this region in the form N2 = {(x, y) : c Sysd:a(y) < a< B(y)} for some choice of functions a and B. Note: You may need to break your region into multiple parts and take unions.
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