Example 6 Video Example )) Evaluate lim x In(x³). x+0+ Solution The given limit is indeterminate because, as x → 0+, the first factor (x) approaches 1 In(x³) approaches-co. Writing x = In(x³) lim x In(x³) = lim 1 x+0+ x+0+ lim = lim x+0+ || X|T|X we have while the second factor → ∞o as x → 0+, so l'Hospital's Rule gives the following. X
Example 6 Video Example )) Evaluate lim x In(x³). x+0+ Solution The given limit is indeterminate because, as x → 0+, the first factor (x) approaches 1 In(x³) approaches-co. Writing x = In(x³) lim x In(x³) = lim 1 x+0+ x+0+ lim = lim x+0+ || X|T|X we have while the second factor → ∞o as x → 0+, so l'Hospital's Rule gives the following. X
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 8E
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Question
Transcribed Image Text:Example 6
Video Example())
Evaluate lim_x In(x³).
x+0+
Solution
The given limit is indeterminate because, as x → 0+, the first factor (x) approaches
1
In(x³) approaches -co. Writing x =
lim_x In(x ³) = lim 1
In(x³)
x=0+.
x+0+
=
=
=
lim
x → 0
lim
x → 0+
1
·=·· we have
IX|T|X
while the second factor
→ ∞ as x → 0*, so l'Hospital's Rule gives the following.
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