Which one of the following is the interval of convergence of the power series 511)n 3n+3 (a) ( 58) (b) 135 135 5' 5 (d) (-00,00) 52 58 Which one of the following is the interval of convergence of the power series 511)n 3n+3 (a) ( 58) (b) 135 135 5' 5 (d) (-00,00) 52 58
4. Three forces of 2 N, 3 N and 4N act as shown below: Calculate the magnitude of the resultant and it's direction relative to the 2 N force. [6.24 N at 76.10°] 4N 60 3N 60° 2 N 1.5 m/s2 at 90° and b 2.6 m/s2 at 145° act at a [2.13 m/s2 at 0°] 5. Acceleration of a point. Draw a diagram and find a - b
7 3n-2 n=1
Prove the following: 1+4+7+...+(3n – 2) n(3n-1) 2
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
5) Test the series for convergence or divergence. n a) In 3n +1 n= b) cos(3n) 1+ (1.2)" n=1
estimate error ∞ 4n (n + 7)3n n = 1
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...
Does sigma (3n^2-n+1)/sqrt(n^7+2n^2+5) converge or diverge using limit comparison test.
Use squeeze theorem an=n^2sin(n)/3n^4+5