3. (i) State precisely what it means that the sequence (x(")) DEN converges to the limit x = R². [5 Marks] (ii) In the Euclidean space R², find the limits of the following sequences (if the limit exists): (a) limn→∞ (n²+1, 1-n); (b) lim∞ (exp(-1/n), exp(-n²)); (c) lim∞ (cos(2πn/3), sin(2πn/3)); 4. In the Euclidean space R2, give example of a sequence: (i) which is located on the quartic parabola x2 many different points, and converges to the limit (2, 16) = [15 Marks] x, contains infinitely [10 Marks] (ii) which includes each of the points (1,0), (1,3), (½³) infinitely - 2 2 many times. [10 Marks]

3. (i) State precisely what it means that the sequence (x(")) DEN converges to the limit x = R². [5 Marks] (ii) In the Euclidean space R², find the limits of the following sequences (if the limit exists): (a) limn→∞ (n²+1, 1-n); (b) lim∞ (exp(-1/n), exp(-n²)); (c) lim∞ (cos(2πn/3), sin(2πn/3)); 4. In the Euclidean space R2, give example of a sequence: (i) which is located on the quartic parabola x2 many different points, and converges to the limit (2, 16) = [15 Marks] x, contains infinitely [10 Marks] (ii) which includes each of the points (1,0), (1,3), (½³) infinitely - 2 2 many times. [10 Marks]

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks