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14. Find lim sup (x_n) where x_n = [n- n(-1)^n -1] / n 15. Find the SET of sequential limits of (x_n) where x n = sin (n(pi)/4)

14. Find lim sup (x_n) where x_n = [n- n(-1)^n -1] / n 15. Find the SET of sequential limits of (x_n) where x n = sin (n(pi)/4)

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.2: Real Numbers
Problem 89E
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14. Find lim sup (x_n) where x_n = [n- n(-1)^n -1] / n 15. Find the SET of sequential limits of (x_n) where x n = sin (n(pi)/4)
Transcribed Image Text:14. Find lim sup (x_n) where x_n = [n- n(-1)^n -1] / n 15. Find the SET of sequential limits of (x_n) where x n = sin (n(pi)/4)
Encoding of numerical answers: (avoid spaces) positive x: type as x negative x: type as -x fraction a over b: type as a/b or as a whole number with exact decimal part ex. 0.5 or 12.34 negative fraction a over b: type as -a/b or as a negative of a whole number w/ exact decimal part ex. -0.5 or -12.34 square root of x: type as sqrt(x) ex. sqrt(2) or as non perfect nth roots sqrt[n] (x) ex. cube root of 10 as sqrt[3] (10) or as irrational numbers such as pi or the euler constant e negative square root of x: type as -sqrt(x) ex. -sqrt(2) (do not put a space between the negative sign and the number) rationalized denominators: instead of 1/sqrt(x) type sqrt(x)/x for typing infinity or negative infinity type infty or -infty (type this if the sequence is divergent but diverges to either infinity or negative infinity) if value does not exist or is undefined: type dne for multiple values enumerate and separate only by commas, in INCREASING ORDER, with no spaces in between: ex. for 1 and 2 and negative 3 over 4, type -2,3/4,1 if you are asked to find a set S, just use the roster method (list elements in increasing order), without spaces, {-2,3/4,1}
Transcribed Image Text:Encoding of numerical answers: (avoid spaces) positive x: type as x negative x: type as -x fraction a over b: type as a/b or as a whole number with exact decimal part ex. 0.5 or 12.34 negative fraction a over b: type as -a/b or as a negative of a whole number w/ exact decimal part ex. -0.5 or -12.34 square root of x: type as sqrt(x) ex. sqrt(2) or as non perfect nth roots sqrt[n] (x) ex. cube root of 10 as sqrt[3] (10) or as irrational numbers such as pi or the euler constant e negative square root of x: type as -sqrt(x) ex. -sqrt(2) (do not put a space between the negative sign and the number) rationalized denominators: instead of 1/sqrt(x) type sqrt(x)/x for typing infinity or negative infinity type infty or -infty (type this if the sequence is divergent but diverges to either infinity or negative infinity) if value does not exist or is undefined: type dne for multiple values enumerate and separate only by commas, in INCREASING ORDER, with no spaces in between: ex. for 1 and 2 and negative 3 over 4, type -2,3/4,1 if you are asked to find a set S, just use the roster method (list elements in increasing order), without spaces, {-2,3/4,1}
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