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Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please help me with both halves of the question with solution so I understand the problems better. Thank you! 

n²
n4 5
Calculate the following limit.
Let an
=
and bn
an
lim =
n→∞ bn
=
n²
an
lim
n→∞ bn
(Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.)
∞
Determine the convergence of an.
n=1
an converges by the Limit Comparison Test because Σ b₁ converges and lim
an
n=1
n=1
n→∞ bn
∞
∞
Σ an diverges by the Limit Comparison Test because Σ bn diverges and lim
an
n=1
n=1
n→∞ bn
∞
Σ an diverges by the Limit Comparison Test because Σ bn diverges.
n=1
n=1
exists and is finite.
is infinite.
Transcribed Image Text:n² n4 5 Calculate the following limit. Let an = and bn an lim = n→∞ bn = n² an lim n→∞ bn (Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.) ∞ Determine the convergence of an. n=1 an converges by the Limit Comparison Test because Σ b₁ converges and lim an n=1 n=1 n→∞ bn ∞ ∞ Σ an diverges by the Limit Comparison Test because Σ bn diverges and lim an n=1 n=1 n→∞ bn ∞ Σ an diverges by the Limit Comparison Test because Σ bn diverges. n=1 n=1 exists and is finite. is infinite.
(Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.)
an
lim =
n→∞ bn
∞
Determine the convergence of Σ an
n=1
∞
an
Σ an converges by the Limit Comparison Test because Σ b, converges and lim
n=1
n=1
n→∞ bn
∞
∞
Σ an diverges by the Limit Comparison Test because Σ bn diverges and lim is infinite.
an
n→∞ bn
n=1
n=1
∞
Σ an diverges by the Limit Comparison Test because Σ bn diverges.
n=1
n=1
exists and is finite.
∞
∞
an
Σan converges by the Limit Comparison Test because Σ be converges and lim
n=1
n=1
n→∞ bn
does not exist.
Transcribed Image Text:(Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.) an lim = n→∞ bn ∞ Determine the convergence of Σ an n=1 ∞ an Σ an converges by the Limit Comparison Test because Σ b, converges and lim n=1 n=1 n→∞ bn ∞ ∞ Σ an diverges by the Limit Comparison Test because Σ bn diverges and lim is infinite. an n→∞ bn n=1 n=1 ∞ Σ an diverges by the Limit Comparison Test because Σ bn diverges. n=1 n=1 exists and is finite. ∞ ∞ an Σan converges by the Limit Comparison Test because Σ be converges and lim n=1 n=1 n→∞ bn does not exist.
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