Assume it is given that T1(n) = O(g1(n)) and T2(n) = O(g2(n)). Prove or disprove each...

Question

Question

Assume it is given that T1(n) = O(g1(n)) and T2(n) = O(g2(n)). Prove or disprove each one of the following claims

T1(n)/T2(n) = O(g1(n)/g2(n))

Answer 1

Answer #1

f(n) = O(g(n)) if there exists a positive integer n₀ and a positive constant c, such that f(n) <= c.g(n) ∀ n >= n₀

Since T1(n) = O(g1(n)) and T2(n) = O(g2(n)), this means

0 <= T1(n) <= c1 * g1(n) -----------> (1)

0 <= T2(n) <= c2 * g2(n) ------------> (2)

a)

Dividing 1 by 2, we have

0 <= T1(n) / T2(n) <= (c1 / c2) * (g1(n) / g2(n))

0 <= T1(n) / T2(n) <= c3 * (g1(n) / g2(n)) where c3 = c1 / c2

Hence, T1(n) / T2(n) = O(g1(n) / g2(n))

Answer 2

Similar Homework Help Questions

2. Let G1, G2, and G3 be groups. Prove the following: a) If G1 = G2,...

2. Let G1, G2, and G3 be groups. Prove the following: a) If G1 = G2, then G2 = 61. b) If G = G2 and G2 = G3, then G =G3.
Q6: For the system shown in Figure below. Calculate the short circuit curTent for a symmetrical phase fault at point F: use a 100MVA base. T1 115 kV TL 50 km 0.4 Ω/km Reactor T2 Power Sys G2 G1&G...

Q6: For the system shown in Figure below. Calculate the short circuit curTent for a symmetrical phase fault at point F: use a 100MVA base. T1 115 kV TL 50 km 0.4 Ω/km Reactor T2 Power Sys G2 G1&G2-75MVA, 10.5kV, 13.2% T1&T2-60MVA, 10.5% Reactor-60MVA, 9% Power Sys-2000MVA, 8000 Q6: For the system shown in Figure below. Calculate the short circuit curTent for a symmetrical phase fault at point F: use a 100MVA base. T1 115 kV TL 50 km 0.4...
Prove or disprove the following: If f(n) =O(g(n)) then nf(n) = O(ng(n))

Prove or disprove the following: If f(n) =O(g(n)) then nf(n) = O(ng(n))

Prove (using the definition of O) or disprove (via counter-example): If f(n) = O(n)), and g(n)...

Prove (using the definition of O) or disprove (via counter-example): If f(n) = O(n)), and g(n) = O(n2), then f(n) + g(n) = O(n5). Prove (using the definition of O) or disprove (via counter-example): If f(n) = O(n), and g(n) = O(n2), then fin)/g(n) = O(n).
No calculations needed, just use written labels given. BUS 1 BUS 2 LINE 1 T1 L1 T2. G1 G2 R= 0.6 pu LINE 2 L2 T3 G3 BUS...

No calculations needed, just use written labels given. BUS 1 BUS 2 LINE 1 T1 L1 T2. G1 G2 R= 0.6 pu LINE 2 L2 T3 G3 BUS 3 a) For the above network, draw positive, negative and zero sequence networks (40 marks) b) Provide the main mathematical steps that will allow you to calculate the magnitude (in ampere) of the phase to ground fault at the midpoint of line 1 As part of your answer you should show clearly,...
Prove or Disprove #3 (d) For each of the following, prove or disprove: iii) There is an element of X × Y with the form (a, 3a) (d) For each of the following, prove or disprove: iii) There is an...

Prove or Disprove #3 (d) For each of the following, prove or disprove: iii) There is an element of X × Y with the form (a, 3a) (d) For each of the following, prove or disprove: iii) There is an element of X × Y with the form (a, 3a)

Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the following conjectures....

Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the following conjectures. f(n) = O(g(n)) implies g(n) = Ω(f(n)) . f(n) = O(g(n)) implies g(n) = O(f(n)). f(n) + g(n) = Θ(min(f(n),g(n))).
BUS 1 BUS 2 LINE 1 T1 L1 T2 G1 G2 R = 0,6 pu LINE 2 L2 T3 G3 BUS 3 a) For the above network, draw positive, negative an...

BUS 1 BUS 2 LINE 1 T1 L1 T2 G1 G2 R = 0,6 pu LINE 2 L2 T3 G3 BUS 3 a) For the above network, draw positive, negative and zero sequence networks (60 marks) b) Provide the main mathematical steps that will allow you to calculate the magnitude (in ampere) of the phase to phase fault current at BUS 1. As part of your answer you should show clearly, on a diagram, how the networks of part (a)...
disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e {a...

disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e {a,b}*} {w w E {a, b}* and no two b's in w have odd number of a's in between}. (b) L2 (c) L3 a" (d) L4 vw n = 3k, for k > 0}. a, b}*} disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e...

(a) Suppose lim(Fm) = 1. Prove or disprove: There exists no E N such that IFml > 0.99 for all o (...

The work provided for part (b) was not correct. (a) Suppose lim(Fm) = 1. Prove or disprove: There exists no E N such that IFml > 0.99 for all o (b) Prove or disprove:If (an) converges to a non-zero real number and (anbn) is convergent, then (bn) is convergent. RUP ) Let an→ L,CO) and an bn→12 n claim br) comvetgon Algebra of sesuenes an (a) Suppose lim(Fm) = 1. Prove or disprove: There exists no E N such that...