Part I. (30 pts) (10 pts) Let fin) and g(n) be asymptotically positive functions. Prove or disprove each of the following statements T a、 f(n) + g(n)=0(max(f(n), g(n))) 1. b. f(n) = 0(g(n)) implies g(n) = Ω(f(n)) T rc. f(n)- o F d. f(n) o(f(n)) 0(f (n)) f(n)=6((f(n))2)
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).
?3: (a). Find the Z-Transform of h(t)-1 (?[n] + fin-1] + ?[n-21 + fin-31) (b). Find the unit impulse response corresponding to the following system (c)Plot the region of convergence and the Z transform for ln"un], where uin- 0 elscwhere and a is
For f(n) = 1000 · 2" and g(n) = 3" we have: g(n) = O(f(n)) O g(n) =(f(n)) O g(n) = 2(f(n))
Show that either g(n) = O(f(n)) or f(n) = O(g(n)) : 1. g(n) = n^2 +7n , f(n) = ^3 -2n^2 2. g(n) = 2n +4 , f(n) = 6lg(n^2)
In the following circuit, the switch has been closed for a long time. At t- o s it moves to open position. What is i(t) for t >0 s? 4. t 0 2 mH 4k Ω 12V (+
ONLY NEED THE SOLUTION TO PARTS E AND F!!!!!!! PLEASE
Analyzing a Fin Consider an infinitely long fin with a square cross section with 5mm. The base of the fin is held at a fixed temperature of To = 100°C and air is passing by the fin at T = 20°C with a convective heat transfer coefficient of h - 55 W/m-K. The fin is made from aluminum with a thermal conductivity of k- 180 W/mK. T. = 20°C n...
Asymptotic notation O satisfies the transitive property i.e. if f(n)=O(g(n)) and g(n)=O(h(n)), then f(n)=O(h(n)). Now we know that 2n =O(2n-1), 2n-1 =O(2n-2?),....... , 2i=O(2i-1?),....... So using rule of transitivity, we can write 2n =O(2i-1?).We can go extending this, so that finally 2n =O(2k?), where k is constant.So we can write 2n =O(1?). Do you agree to what has been proved?If not,where is the fallacy? 6 marks (ALGORITHM ANALYSIS AND DESIGN based problem)
is these true or false ?and explain why a)if f(n)=O(g(n)) then 2^(f(n)=O(2^(g(n)))... please solve without lim b)if f(n)=o(g(n)) then 2^(f(n)=o(2^(g(n)))... please solve without lim
Solving for The switch in the
circuit below has been closed for a long time and it opens at t =
0. Find the following:
for b) can you solve it without using Laplace transform? As in
no s domain, thank you
1. The switch in the circuit below has been closed for a long time and it opens at t = 0. Find the following: (a) (20 points) v(0%), and v.(0%) for t < 0. (b) (20 points) v(t),...