Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Let f (n) and g(n) be functions mapping nonnegative integers to real numbers. We

ID: 3798305 • Letter: L

Question

Let f (n) and g(n) be functions mapping nonnegative integers to real numbers. We say that f (n) is (g(n)) if there is a real constant c > 0 and an integer constant n0 1 such that for all n n0 , f (n) c g(n). Show that n2 is (nlog n) by specifying the constants c and n0 Let f (n) and g(n) be functions mapping nonnegative integers to real numbers. We say that f (n) is (g(n)) if there is a real constant c > 0 and an integer constant n0 1 such that for all n n0 , f (n) c g(n). Show that n2 is (nlog n) by specifying the constants c and n0 Let f (n) and g(n) be functions mapping nonnegative integers to real numbers. We say that f (n) is (g(n)) if there is a real constant c > 0 and an integer constant n0 1 such that for all n n0 , f (n) c g(n). Show that n2 is (nlog n) by specifying the constants c and n0

Explanation / Answer

for n 1

n > logn

Multiplying with n on both sides

n2 > nlogn

So for c = 1 and n0 = 1, we have proved that n2 is (nlogn)

Related Questions

Let a1, a2, . . . , an be a sequence of positive integers. An increasing subsequ
Question #3639681
Let aR and let f and g be real functions defined at all points x in some open in
Question #1944059
Let a^2 be an integer. Prove that a^2 is divisible by 5 if and only if a is divi
Question #3036714
Let a^2 be an integer. Prove that a^2 is divisible by 5 if and only if a is divi
Question #3036715
Let a_1 = [1 2 4], a_2 = [1 3 5]. (a) Explain if the following vector b_1 = [2 5
Question #3038847
Let a_1, a_2, ..., a_n be real numbers with |a_k| lessthanorequalto M for each k
Question #3108892
Let a_1, a_2, a_3, ...., a_p and b be vectors in R^n and A = [a_1 a_2 a_3, ...,
Question #3036234
Let a_n = a_n-1 + 6a_n-3. Select all that applies. a_n is of degree 2 a_n is of
Question #3119741

Navigate

Previous
Let f ( x ) be the probability density function for the lifetime of a manufactur
Next
Let f (r) 13-T The slope of the tangent line to the graph of f r) at the point (

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.