Let f(n) = 5n4 + 3n3 − 5. Show that f(n) is Θ(n4) by directlyfinding the constants k, C1, and C2
Answer
Answer: k = 3, C1 = 1 and C2 = 6Explanation:————–f(n) = Θ (g(n)) means there are positive constants c1, c2, and k, such that 0 ≤ c1g(n) ≤ f(n) ≤ c2g(n) for all n ≥ k. The values of c1, c2, and k must be fixed for the function f and must not depend on n.5n4 + 3n3 − 5 = (n^4)=> c1(n^4) <= 5n4 + 3n3 − 5 <= c2(n^4)Let’s assume c1 = 1
OR
OR