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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![Giving the series,
In|1–x|
Use the series and some calculus to develop a series for In|1-x]. Hint: What operation takes
1-x
1
dx
= 0+1+2x+3x²+
1 2
· = 1 + x + x² + x
In|1-x)=√√√₁²x
= 0+1+2x+3x²+
2
X
=x+=+
2
1
1-x
3
² In|1-x| = — _—_dx = S(
- dx =
3
X
+
+
3 4
d
dx
·(1+x+x²+x³+ .....)
+
= S( 1 + x + x ² + x ²³+ +.....) dx
+C
in|1-x| = S _—_—_—_dx= [ {(1+x+x² + x³² + ....) dx
- X
+C
1 1
1
+ + + + + + +
X
+ C
....dex
+ C
1
1- x
10
to In |1-x|?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30fc4209-43ac-409b-8363-1a56de792bf2%2F14e44989-2311-4389-99b3-f12b86fadacf%2Fe7nr8cm_processed.png&w=3840&q=75)
Transcribed Image Text:Giving the series,
In|1–x|
Use the series and some calculus to develop a series for In|1-x]. Hint: What operation takes
1-x
1
dx
= 0+1+2x+3x²+
1 2
· = 1 + x + x² + x
In|1-x)=√√√₁²x
= 0+1+2x+3x²+
2
X
=x+=+
2
1
1-x
3
² In|1-x| = — _—_dx = S(
- dx =
3
X
+
+
3 4
d
dx
·(1+x+x²+x³+ .....)
+
= S( 1 + x + x ² + x ²³+ +.....) dx
+C
in|1-x| = S _—_—_—_dx= [ {(1+x+x² + x³² + ....) dx
- X
+C
1 1
1
+ + + + + + +
X
+ C
....dex
+ C
1
1- x
10
to In |1-x|?
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