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3. (i) State precisely what it means that the sequence (x (n)) DEN Converges to the limit xЄ R². [5 Marks] (ii) In the Euclidean space R2, find the limits of the following sequences (if the limit exists): 1-n (a) lim, (+11); n (b) lim (exp(−1/n), exp(−n²)); (c) lim∞ (cos(2πn/3), sin(2π/3)); [15 Marks]

3. (i) State precisely what it means that the sequence (x (n)) DEN Converges to the limit xЄ R². [5 Marks] (ii) In the Euclidean space R2, find the limits of the following sequences (if the limit exists): 1-n (a) lim, (+11); n (b) lim (exp(−1/n), exp(−n²)); (c) lim∞ (cos(2πn/3), sin(2π/3)); [15 Marks]

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 48E
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3. (i) State precisely what it means that the sequence (x (n)) DEN Converges to the limit xЄ R². [5 Marks] (ii) In the Euclidean space R2, find the limits of the following sequences (if the limit exists): 1-n (a) lim, (+11); n (b) lim (exp(−1/n), exp(−n²)); (c) lim∞ (cos(2πn/3), sin(2π/3)); [15 Marks]
Transcribed Image Text:3. (i) State precisely what it means that the sequence (x (n)) DEN Converges to the limit xЄ R². [5 Marks] (ii) In the Euclidean space R2, find the limits of the following sequences (if the limit exists): 1-n (a) lim, (+11); n (b) lim (exp(−1/n), exp(−n²)); (c) lim∞ (cos(2πn/3), sin(2π/3)); [15 Marks]
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