College Algebra
College Algebra
1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: OpenStax
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![画像: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), (1⁄23) infinitely - 2 2 many times. [10 Marks]](https://content.bartleby.com/qna-images/question/39a0c022-e49a-477b-ab1a-da6fafebfbe8/a52d53fc-937d-406c-8896-770ae5be6ae2/i6ep4jf_thumbnail.jpeg){kind=link}
Transcribed Image Text: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), (1⁄23) infinitely
-
2
2
many times.
[10 Marks]
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