Determine whether the following maps are immersion and submersion. ((((please please pleaseeeee please answer with detalis and do not copy another solution. (i'll give a thumbs up) i don't understand how to prove a map is immersion or submersion. i need to see your detalis so i can understand. )))). thank you. (1) f :R → R², f(r) = (x², x) (2) f : R → R², f(x) = (x*, x²) (3) f : S' → R², f(r, y) = (x² – y², 2ry) (4) f: S2 → S2, f(r, y, z) = (y, z, x) (5) f: S2→R2, f(r, y, 2) = (y, 2) (6) f : S² → R°, f(x, y, 2) = (y, 0, z, 0, a) (7) f : S² → Rº, f (x, y, z) = (x², y², z², ry, yz, za) (8) f : S² → R³, f(x, y, z) = (2x, 3y, 42) %3D (9) R → S' × S', f(x) = ((cos r, sin r), (cos T2, sin 72)) %3D
Determine whether the following maps are immersion and submersion. ((((please please pleaseeeee please answer with detalis and do not copy another solution. (i'll give a thumbs up) i don't understand how to prove a map is immersion or submersion. i need to see your detalis so i can understand. )))). thank you. (1) f :R → R², f(r) = (x², x) (2) f : R → R², f(x) = (x*, x²) (3) f : S' → R², f(r, y) = (x² – y², 2ry) (4) f: S2 → S2, f(r, y, z) = (y, z, x) (5) f: S2→R2, f(r, y, 2) = (y, 2) (6) f : S² → R°, f(x, y, 2) = (y, 0, z, 0, a) (7) f : S² → Rº, f (x, y, z) = (x², y², z², ry, yz, za) (8) f : S² → R³, f(x, y, z) = (2x, 3y, 42) %3D (9) R → S' × S', f(x) = ((cos r, sin r), (cos T2, sin 72)) %3D
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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(please answer first four parts i will give thumbs up)
Transcribed Image Text:Determine whether the following maps are immersion
and submersion.
((((please please pleaseeeee please answer with
detalis and do not copy another solution. (i'll give a
thumbs up)
i don't understand how to prove a map is immersion or
submersion. i need to see your detalis so i can
understand. ))). thank you.
(1) f :RR, f(x) = (x², x)
(2) f : R → R², f(x) = (x*, x²)
(3) f : S' → R°, f(z, y) = (x² – y², 2ry)
(4) f : S² → S², f(r, y, 2) = (y, z, x)
(5) f : S² → R2, f(x, y, z) = (y, z)
(6) f : S² → Rº, f(x, y, 2) = (y, 0, z, 0, x)
%3D
(7) f : S² → Rº, f(x, y, z) = (x², y², 2², ry, yz, za)
(8) f : S² → R³, ƒ (x, y, 2) = (2x, 3y, 42)
%3D
%3!
(9) R → S' x S', f(r) = ((cos r, sin z), (cos TI, sin 72))
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