State the excluded values for the following expression. Then simplify the expression. Show all work. n +11n + 24 n2-3n- 18
Simplify each expression. Thanks 4n 6 n-3 2n 7) a+4_6 2a +6 2 8) 9) x+5 x +3 10) 6 r-6 r+ 3
2. Simplify: (n + 2)! (1) n! (2n-1)! (2) (2n + 1)! (2n + 2)! (3) (2n)!
Problem 1. Find the following limits. sinn (1) Vn2+1 (2) Vn2 +1. 31 n10 + n2 10° + na 2n² + 3n sinn 7n2 + 8n +9cos n (6) sin(TV n2 +1).
Simplify each expression assuming that n is an integer and n 2 2. a) (n+ 1) 31(n-2) b) (n+ 3)! (n+1)! . (Please show all work with steps and all parts listed) T MacBook Air
Order the following functions by asymptotic growth rate. 2n log n + 2n, 210, 2 log n, 3n + 100 log n, 4n, 2n, n2 + 10n, n3, n log n2
Which of these sequences are convergent? (Select all that apply) (A) An= _cos (2n) 5" g" (B) (n = 78 + 4 2n + (-1)"5 8n - (-1)"4 (D) «= (-2)" 2" + m3 (E) (n = 3 + 4" (F) (n = cos SAMSUNG
Help with any of these? Practice Problems 31 n* cos n 12 23. Σ㈠)"21/" 32n-1 n(ln n)3 n-2 24 + 5 -1 In n 25, Σ(-1)" 15 35 та і 36 (2n)" 16 26 17. Σ5n3nn Σ-π)" 7. k 27, 37 n-I E1 28. +1 10 k + 5 18 19 39 2.5.8(3n + 2)T ㄒㄧ- Σ(阪-1) 10 30 40 8m - 5 '고 (n + 1) (n-2) Practice Problems 31 n* cos n 12 23. Σ㈠)"21/" 32n-1 n(ln n)3...
Prove by Induction 24.) Prove that for all natural numbers n 2 5, (n+1)! 2n+3 b.) Prove that for all integers n (Hint: First prove the following lemma: If n E Z, n2 6 then then proceed with your proof.
a) Prove that running time T(n)=n3+30n+1 is O(n3) [1 mark] b) Prove that running time T(n)=(n+30)(n+5) is O(n2) [1 mark] c) Count the number of primitive operation of algorithm unique1 on page 174 of textbook, give a big-Oh of this algorithm and prove it. [2 mark] d) Order the following function by asymptotic growth rate [2 mark] a. 4nlogn+2n b. 210 c. 3n+100logn d. n2+10n e. n3 f. nlogn