10. Find the limit (if it exists) of the sequence (x_n) where x_n= cos(n)/n.

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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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}
10. Find the limit (if it exists) of the sequence
(x_n) where x_n= cos(n)/n.
11. For the sequence (x_n) where x_1>3 and
x_(n+1) = 2-sqrt(x_n-2), if x_n→x as
n→∞ then find x.
12. Find the SET of sequential limits of 3-
(-1)^n
13. Find lim inf (x_n) where x_n = 2+
(-1)^{3n}
Transcribed Image Text:10. Find the limit (if it exists) of the sequence (x_n) where x_n= cos(n)/n. 11. For the sequence (x_n) where x_1>3 and x_(n+1) = 2-sqrt(x_n-2), if x_n→x as n→∞ then find x. 12. Find the SET of sequential limits of 3- (-1)^n 13. Find lim inf (x_n) where x_n = 2+ (-1)^{3n}
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