or each of the f(n) in Exercises 4-12, give the letter of the best estimate amon

Question

or each of the f(n) in Exercises 4-12, give the letter of the best estimate among the following (a) f(n) Olnn) (b) fn) O(ln?n); (d) f(n) = 0(n); (e) f(n) =O(n2); (g) f(n) = 0(2"); (h) f(n) = 0(n!); (e) f(n) O(ln3n); (f) f(n)=0(n3); (i) f(n) = O(nn), n ! 4. The number of ways there are to choose 3 distinct items from a set of n items. o 5. 101n3 n +20n2. e 6. The number of monomials in a, y, z of total degree at most n. 7. The area of a fixed shape after it's magnified by a factor of n. 8. The amount of memory space a computer requires to store the number n. 9. The amount of memory space a computer requires to store n2 10. The sum of the first n positive integers. t 11. The sum of the squares of the first n positive integers. n 12. The number of bits (base-2 digits) in the sum of the squares of the first n positive integers. ol.

Explanation / Answer

According to chegg policy you should have give only one question . you gave so many questions. So I just give you answer of first 2 questions.

4) First Item Will be choosen from n items in n ways.

Next , second item can choose from remaining (n-1) items is (n-1) ways.

Nad third items can Be choose from remaining (n-2) items in (n-2) ways .

So total ways = n*(n-1)*(n-2)=n^3-3n^2+2n = O(n^3)

Hence option f .

.

5)

we lave (ln(x))^3 <x^2 for all x>1 .

Hence (ln(x))^3 +x^2 = O(x^2)

Note: Our aim is that to find the largest term which ill be big O

Thx

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