In(n) n a. Calculate the first 10 terms of this sequence. Based on these calculations, do you think the sequence converges or diverges? Why? b. For this sequence, there is a corresponding continuous function ƒ defined by f(x) = In(x) x Draw the graph of f(x) on the interval [0,10] and then plot the entries of the sequence on the graph. What conclusion do you think we can draw about the sequence {¹n(n)} if limx→∞ f (x) = L? Explain. c. Note that f(x) has the indeterminate formas x goes to infinity. What idea from differential calculus can we use to calculate limx→∞ f (x)? Use this method to find limx→∞ f (x). What, then, is limɲ→∞ In(n)? n
In(n) n a. Calculate the first 10 terms of this sequence. Based on these calculations, do you think the sequence converges or diverges? Why? b. For this sequence, there is a corresponding continuous function ƒ defined by f(x) = In(x) x Draw the graph of f(x) on the interval [0,10] and then plot the entries of the sequence on the graph. What conclusion do you think we can draw about the sequence {¹n(n)} if limx→∞ f (x) = L? Explain. c. Note that f(x) has the indeterminate formas x goes to infinity. What idea from differential calculus can we use to calculate limx→∞ f (x)? Use this method to find limx→∞ f (x). What, then, is limɲ→∞ In(n)? n
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 71E
Related questions
Question
show full and complete procedure
![In(n)
n
a. Calculate the first 10 terms of this sequence. Based on these calculations, do you
think the sequence converges or diverges? Why?
b. For this sequence, there is a corresponding continuous function f defined by
f(x) =
In(x)
x
Draw the graph of f(x) on the interval [0, 10] and then plot the entries of the
sequence on the graph. What conclusion do you think we can draw about the
sequence {In(n)} if limx→∞ f (x) = L? Explain.
c. Note that f(x) has the indeterminate formas x goes to infinity. What idea from
differential calculus can we use to calculate limx→∞ f (x)? Use this method to find
limx→∞ f (x). What, then, is limŋ→∞
In(n)?
n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F704e3954-aed4-49bb-91f4-2bda230b35b6%2Fb6817f8b-a87c-4a6d-9af4-b0c9fbd0a883%2F2dxkl7m_processed.png&w=3840&q=75)
Transcribed Image Text:In(n)
n
a. Calculate the first 10 terms of this sequence. Based on these calculations, do you
think the sequence converges or diverges? Why?
b. For this sequence, there is a corresponding continuous function f defined by
f(x) =
In(x)
x
Draw the graph of f(x) on the interval [0, 10] and then plot the entries of the
sequence on the graph. What conclusion do you think we can draw about the
sequence {In(n)} if limx→∞ f (x) = L? Explain.
c. Note that f(x) has the indeterminate formas x goes to infinity. What idea from
differential calculus can we use to calculate limx→∞ f (x)? Use this method to find
limx→∞ f (x). What, then, is limŋ→∞
In(n)?
n
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