1. Give an asymptotically tight bound to each of the following expressions: 3n^2 + 2n^3 3n log n + 2n^2 2^n + 3^n 2. Arrange the following asymptotic family from lower order to higher order. The first has been done for you. O(n log n) O(n^3) O(log n) O(n^2 log n) O(n) O(3^n) O(2^n) 3. At work, Peter needs to solve a problem of different sizes. He has two algorithms available to solve the problem. Algorithm A can solve the...
Find general solution for the recurrence relation: an = 6an−1−9an−2+ 2 × 3n + 4 × 2n
Does sigma (3n^2-n+1)/sqrt(n^7+2n^2+5) converge or diverge using limit comparison test.
Find the sum of the series. n! n0 3n+1x2n + -/0.7 points SCalcET8 11.10.077. Find the sum of the series. 32n+ (2n 1)! n0 Find the sum of the series. n! n0 3n+1x2n + -/0.7 points SCalcET8 11.10.077. Find the sum of the series. 32n+ (2n 1)! n0
1. h(a) = -a2-a g(a) = 2a+1 Find (h-g)(-4) 2. f(n) = 2n +4 g(n) = 3n-1 Find (f+g)(-3)
1. Simplify each expression, for n = 5 a) 8n + 2 b) n2 - 2n+n d) 19 - 3n + e) (3n - 3) + 15-n-18
Among the following series, which one does converge conditionally? n=1 Σ(-1)"re-n 1-3-5 3 3-5 3-5.7 1-3-5(2n-1 -(2n) 1.3.5 (2n-1) (-1)" n=1 Σ(-1)"re-n 1-3-5 3 3-5 3-5.7 1-3-5(2n-1 -(2n) 1.3.5 (2n-1) (-1)"
Determine whether the following series is absolutely convergent, conditionally convergent, or divergent. (–1)n-1((In n) 2n (3n+4)n • State the name of the correct test(s) that you used to reach the correct conclusion. • Show all work. • State your conclusion.
Please note n's are superscripted. (a) Use mathematical induction to prove that 2n+1 + 3n+1 ≤ 2 · 4n for all integers n ≥ 3. (b) Let f(n) = 2n+1 + 3n+1 and g(n) = 4n. Using the inequality from part (a) prove that f(n) = O(g(n)). You need to give a rigorous proof derived directly from the definition of O-notation, without using any theorems from class. (First, give a complete statement of the definition. Next, show how f(n) =...
Use the definition of 0 to show that 5n^5 +4n^4 + 3n^3 + 2n^2 + n 0(n^5).Use the definition of 0 to show that 2n^2 - n+ 3 0(n^2).Let f,g,h : N 1R*. Use the definition of big-Oh to prove that if/(n) 6 0(g{n)) and g(n) 0(h{n)) then/(n) 0(/i(n)). You should use different letters for the constants (i.e. don't use c to denote the constant for each big-Oh).