# Prove or disprove: a) f(n) = 2^n + 1 = O(2^n) b) f(n) = 2^n + 1 = theta (2^n) c) f(n) = 2^2n = O(2^n) d) f(n) = 2^2n = theta (2^n)…

ONLY DO PART C AND D

Part c is incorrect, hence need to be disproved.

c) f(n) = 2^2n = O(2^n)

Don't use plagiarized sources. Get Your Custom Essay on
Prove or disprove: a) f(n) = 2^n + 1 = O(2^n) b) f(n) = 2^n + 1 = theta (2^n) c) f(n) = 2^2n = O(2^n) d) f(n) = 2^2n = theta (2^n)…
Get an essay WRITTEN FOR YOU, Plagiarism free, and by an EXPERT!

Big O describes an upper limit on the growth behaviour of a function, for example the runtime of a program, when inputs become large. So for function f(x) = log(n), or f(x) = n, both are O(n^2), because both are always smaller than n^2. This is due to the fact that Big O notation gives us the upper bound, which need not to be the just greater than the exact function.

Hence for Part c, we can see easily that 2^2n is always greater than 2^n, hence f(n) can’t be O(2^n) in any case.

Similarly for part D, it is correct.

for Theta notation, the function gives us the lower bound, which means for f(n) = log(n) or f(n) = n, for both, the lower bound can be theta(1), because 1 is always lesser than log(n) or n;

So for part d, as 2^n is always lesser than 2^2n, hence we can safely say that

f(n) is theta(2^n).

Order NOW For a 10% Discount!
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

## Calculate the price of your order

Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

## Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.