3. Evaluate each of the following limits. 4n? - n +5 (a) an = (-1)","; (b)...
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).
12. Determine whether the following series converge or diverge. (a) (b) 2-nzn-1 4n n=0 n=1 4n (-1)n+1 loge n (c) (d) 7n + 1 n n=1 n=3 iM: M: Mį M8 sinn (e) ✓n n2 + 2 (f) n2 n=1 n=1 2n en (g) (h) Vn! n=1 n=1
• Find a simplified expression for C14). (-1)"5.9.13 .....(4n - 5) -5) (B) (-1) (-1)"-15.9.13..... (4n-3) 4" n! 41-1 n! (-1)"4.8.12.....(4-4) In - 4) (E) (-1) 11... • (An - 3) 4" n! 4"n! (-1)"-13.7.11 .....(4n - 5) (-1)"-14.8.12.....(4n-4) (G) 4h n! 4n-1n! (-1)"5.9.13. ....(4 -3) 4"n! (-1)"3.7.11 ... • (4n - 5) 4"-1 n!
'4n+5\n Test the following series for convergence. In=1 5n+6
1. a) Let f(n) = 6n2 - 100n + 44 and g(n) = 0.5n3 . Prove that f(n) = O(g(n)) using the definition of Big-O notation. (You need to find constants c and n0). b) Let f(n) = 3n2 + n and g(n) = 2n2 . Use the definition of big-O notation to prove that f(n) = O(g(n)) (you need to find constants c and n0) and g(n) = O(f(n)) (you need to find constants c and n0). Conclude that...
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
Match the portion of the Cartesian graph that corresponds to the labeled portions of the polar graph. M 1 5 N 1/4 1/2 34/4 TC 5704 371/2 77/4 21 2 (3) 6 7) Р a) 2M, 4N, 7P b) 3P, 6N, 7M, c) 2M, 5N, 7P d) 2P, 6N, 7M, e) 1M, 3N, 6P f) 2P, 6N , 8M g) 2P, 4N, 7M h) 3P, 4N, 6M i) 4N, OM, 7P j) 1M, 3P, 4N
convergence of 2:58-(3n-1) 3.7-11.(4n-1) o0 2.5.8 (3n-1) (x 1) Find the radius of convergence of A. B. 4/3 C. 3/4 I),2 D. O E. 3/2 O F. 1/2 О н. 2/3 convergence of 2:58-(3n-1) 3.7-11.(4n-1) o0 2.5.8 (3n-1) (x 1) Find the radius of convergence of A. B. 4/3 C. 3/4 I),2 D. O E. 3/2 O F. 1/2 О н. 2/3
Simon Shania Tate Navdeep C = 4n + 1 C = 3n + 4 + n-3 C = (n + 1) + (-2n) C = 2(2n + 3) - 5 Use algebra skills to determine which of these four equations are equivalent. Show your work.
16. Order the following functions from lowest to highest 0-class. fs= 4n /n+2n2 - fonlg (n')-lg (n'3) f2- 3n -lg (lg (n)) + n°.5 fs=3n3- 2n2 +4n - 5 f, 31459 + 1.5n lg (n) f=1.2" - 0.8" +2n2 16. Order the following functions from lowest to highest 0-class. fs= 4n /n+2n2 - fonlg (n')-lg (n'3) f2- 3n -lg (lg (n)) + n°.5 fs=3n3- 2n2 +4n - 5 f, 31459 + 1.5n lg (n) f=1.2" - 0.8" +2n2