Using L'Hôpital's rule one can verify that In x lim x-+x x XT == 0, lim x+x ln x = lim x ln x = 0 x―0+ for any positive real number r. (a) Use these results, as necessary, to find the limits of f(x) = x² ln(3x) as x +∞ and as x → 0+. lim x2ln(3x) = x-+00 lim x² In(3x) = x➡0+ (b) Graph f(x) = x² ln(3x) and identify the relative extremum and inflection point. f(x) has a relative Choose one▾ at the point (,) f(x) has inflection point (, )
Using L'Hôpital's rule one can verify that In x lim x-+x x XT == 0, lim x+x ln x = lim x ln x = 0 x―0+ for any positive real number r. (a) Use these results, as necessary, to find the limits of f(x) = x² ln(3x) as x +∞ and as x → 0+. lim x2ln(3x) = x-+00 lim x² In(3x) = x➡0+ (b) Graph f(x) = x² ln(3x) and identify the relative extremum and inflection point. f(x) has a relative Choose one▾ at the point (,) f(x) has inflection point (, )
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
Question
![Using L'Hôpital's rule one can verify that
In x
lim
x-+x x
XT
== 0,
lim
x+x ln x
=
lim x ln x = 0
x―0+
for any positive real number r.
(a) Use these results, as necessary, to find the limits of
f(x) = x² ln(3x) as x +∞ and as x → 0+.
lim x2ln(3x) =
x-+00
lim x² In(3x) =
x➡0+
(b) Graph f(x) = x² ln(3x) and identify the relative extremum
and inflection point.
f(x) has a relative Choose one▾
at the point (,)
f(x) has inflection point (, )](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F342015f0-19e8-40cd-98ef-dc8b52ff501d%2F7c8a8de9-319c-4caa-baba-04b703d95bac%2Fdnlvtc7_processed.png&w=3840&q=75)
Transcribed Image Text:Using L'Hôpital's rule one can verify that
In x
lim
x-+x x
XT
== 0,
lim
x+x ln x
=
lim x ln x = 0
x―0+
for any positive real number r.
(a) Use these results, as necessary, to find the limits of
f(x) = x² ln(3x) as x +∞ and as x → 0+.
lim x2ln(3x) =
x-+00
lim x² In(3x) =
x➡0+
(b) Graph f(x) = x² ln(3x) and identify the relative extremum
and inflection point.
f(x) has a relative Choose one▾
at the point (,)
f(x) has inflection point (, )
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