Let 2, be the region bounded by the curves y = r|r| and y =r. Write this region in the form %3D N2 = {(z, y) : a
Let 2, be the region bounded by the curves y = r|r| and y =r. Write this region in the form %3D N2 = {(z, y) : 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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Plz solve correctly part 2 only plz correctly and take a thumb up plz
![Numeracy 4. Some regions 2 in R2 can be written down by describing the functions which form their boundaries.
For example, the set = {(r,y) : -1<I<2,-1-rSy s1-r²} is drawn below:
y = 1-r
y = -1-r
I=1
Hence, if z = 1 (as shown in the diagram) then the set describes all possible y-values between -1-r = -1-(1) = -2
and 1- z = 1- (1)² = 0.
1.
Draw the region
= {(r, y) : 0 <*<1:1-rSy<2-(*- 1)²} u {(z, y) : 1<*< 2:1-1<y52-(*-1)*}
No explanation is required.
2.
Let 2, be the region bounded by the curves y = r|r| and y = r. Write this region in the form
N2 = {(r, y) : a <Isb: f(r) <y Sg(z)}
for some choice of functions f and g. Note: You may need to break your region into multiple parts and take
unions.
3.
et 2 be the same region as in part (2). Write this region in the form
N = {(r, y) : c<y <d: a(y) << B(u)}
for some choice of functions a and 8. Note: You may need to break your region into multiple parts and take
unions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2409818e-0ef7-422d-b1ad-48b83a65fc9d%2Fb78a4994-49c8-4849-8d70-26cb98b8bc3a%2F1izhcx7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Numeracy 4. Some regions 2 in R2 can be written down by describing the functions which form their boundaries.
For example, the set = {(r,y) : -1<I<2,-1-rSy s1-r²} is drawn below:
y = 1-r
y = -1-r
I=1
Hence, if z = 1 (as shown in the diagram) then the set describes all possible y-values between -1-r = -1-(1) = -2
and 1- z = 1- (1)² = 0.
1.
Draw the region
= {(r, y) : 0 <*<1:1-rSy<2-(*- 1)²} u {(z, y) : 1<*< 2:1-1<y52-(*-1)*}
No explanation is required.
2.
Let 2, be the region bounded by the curves y = r|r| and y = r. Write this region in the form
N2 = {(r, y) : a <Isb: f(r) <y Sg(z)}
for some choice of functions f and g. Note: You may need to break your region into multiple parts and take
unions.
3.
et 2 be the same region as in part (2). Write this region in the form
N = {(r, y) : c<y <d: a(y) << B(u)}
for some choice of functions a and 8. Note: You may need to break your region into multiple parts and take
unions.
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