5. Let ф: S1 S2 be a diffeomorphism. a. Show that S is orientable if and only if S2 is orientable (thus, orientability is preserved by diffeomorphisms). b. Let S, and S2 be orientable and oriented. Prove that the diffeomorphism ф induces an orientation in S. Use the antipodal map of the sphere (Exercise 1, Sec. 2-3) to show that this orientation may be distinct (cf. Exercise 4) from the initial one (thus, orientation itself may not be preserved by...
3. Show that if S, and S2 are Jordan measurable, then so are Si U S2 and Sin S2.
find. inverse Laplace transfer show step buy step soultion
+8 (b) s(+16) 2s3 3s +6s+4 (s2 +4)(s2 +2s+2) (c) +3s + (d) 2 2 1 s-2s +s (e) (s+2)e (f 2s +1 22-6s3 (g) -3s +2 2(s22r4) (24) (h) 2 (i) (2s+1 ($2+8)e (i) (216)
+8 (b) s(+16) 2s3 3s +6s+4 (s2 +4)(s2 +2s+2) (c) +3s + (d) 2 2 1 s-2s +s (e) (s+2)e (f 2s +1 22-6s3 (g) -3s +2 2(s22r4) (24) (h) 2 (i) (2s+1 ($2+8)e (i)...
2. The transfer function of a CT LTI system is given by H(s) (s2 +6s +10) (s2 -4s +8) a) Draw the pole-zero plot of the transfer function. b) Show all possible ROC's associated with this transfer function. c) Obtain the impulse response h(t) associated with each ROC of the transfer function. d) Which one (if any) of the impulse responses of part c) is stable?
2. The transfer function of a CT LTI system is given by H(s) (s2...
1. Let S and S2 be bounded sets in R", and let f : SU S2 + R be a bounded function. Show that if f is integrable over S, and S2, then f is integrable over Si S2, and Janson = Sesia f - Soins f. Sins2
How to prove it
lim exists if and only if S1 S2
lim exists if and only if S1 S2
For the following reactions, determine the mechanism(s), Sy1, S2, E1 or E2. Show the mechanism(s) and determine the product(s). Indicate major product if one is present. Include stereochemistry at stereogenic centers. KOC(CH3)a Br 12. CH3CH2OH 13. Cl он
QUESTION 11 The SI unit of the angular acceleration is rad/s2 rad/s m/s m/s2
Find a minimal representation for the system G (s) s2 = [ s+1 (s+2)(8+3) $2+38+2 1
8. The velocity of the ant at t = 10 s is: a. 50 cm/s b. 0.4 cm/s c. 5.0 cm/s d. 6.0 cm/s The velocity v: (in m/s) of an object is given by the equation V; = 4t +3, where t is the time in seconds. Answer questions 9 and 10 based on this equation. 9. The displacement of the object between t 1 s and t = 2 sis: a. 5 m c. 9 m b. 7...