Question

Part 3 - Big-Theta 15pts For the following problem, give and prove the Big-Oh, Big-Omega, and thus the Big-Theta of the function. Provide a graph for both the Big-Oh and Big-Omega inequalities with the constants you chose. You may use wolframalpha.com or any other graphing site to achieve this.

Show that f(n)= 18n+4 is in Θ(n).

Explain your analysis.  

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

Let f(n)=18*n+4

So,

f(n)=18*n+4<=18*n+4*n=(22*n) for all n>=1

So,

f(n)<=22*n for all n>=1

So,

let c1=22 and n0=1

So,

f(n)<=c1*n for all n>=n0

Also,

f(n)>=18*n for all n>=1

Let c2=18

So,

c2*n<=f(n)<=c1*n for all n>=n0

So,

f(n)=theta(n)

Kindly revert for any queries

Thanks.