estimate error
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2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
2) Prove convergence of In} using the Squeeze lemma: n2-3n+7 a) In = 73 - 4n - 1
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
3. Evaluate each of the following limits. 4n? - n +5 (a) an = (-1)","; (b) an= n+1 3n2+1 n n+1 (c) an= 5n (d) ann +1 n 3n (e) an=- () 4n = 5 - n+1 1.1" (g) an= (h) an= (-1)" 2 - 1 n
Prove the following: 1+4+7+...+(3n – 2) n(3n-1) 2
7 3n-2 n=1
7T13 7m x-_ 뜨 11. (10 points) Suppose the infinite series n=1 4n-1+1 is approximated by the partial sum n=1 4n-41. Estimate how large k needs to be in order for the error to be no larger than 10
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).
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