Let x E (-1,0) and let R, (x) be the remainder in Maclaurin's formula for In(1 + x) in Cauchy's form. Write down the formula for R, (x). This formula should contain three variables, n, x and, where & E (x, 0). R₁(x) = Put Qn(x) = (1 + 5)|x-¹|R, (x)|. Based on the above formula for R, (x), find the smallest constant a such that Qn(x) ≤alx". a=
Let x E (-1,0) and let R, (x) be the remainder in Maclaurin's formula for In(1 + x) in Cauchy's form. Write down the formula for R, (x). This formula should contain three variables, n, x and, where & E (x, 0). R₁(x) = Put Qn(x) = (1 + 5)|x-¹|R, (x)|. Based on the above formula for R, (x), find the smallest constant a such that Qn(x) ≤alx". a=
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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Solve b,c,d
Don't copy paste from chegg
![1:53 ✓
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Given the function is
f(x) = ln (1+x)
Step 2
Now
f(x) = ln (1 + x)
f'(x) = ₁⁄² x
1+x
ƒ” (x)
f" (x)
f""" (x)
f"'""" (x)
Step 3
=
Then
Rn (x)
Rn (x)
Rn (x)
=
ƒn (x)
fn+1(x)=
=
Rn (x)
|||
=
=
-
=
=
=
1
(1+x)²
2
(1+x)³
6
(1+x) 4
24
(1+x)5
(-1)^-¹(n-1)!
(1+x)"
ASK
=
(-1)^n!
(1+x)n+1
(-1)^n!
(1+g)n+1
(n+1)!
2!
(1+x)³
(1+x)³
fn + 1 (§)
· ( x
- §) n+1
(n+1)!
4!
(-1)^n!
(1+) n+¹ (n+1)n!
3!
(1+x)*
(-1)"n!
(1+ ε) n+¹ (n+1)
Vo))
LTE 1.1 LTE2 4+1 9%
+ [9]
(x − (− 1)) ¹+¹
·
√x MATH SOLV
(x + 1)^+1
(x + 1)n+¹](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf9c0aa8-f0c2-40a6-a625-b5a0e0c97da9%2F78a25793-6603-4178-8e64-458becef1e34%2F5l387t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1:53 ✓
bartleby.com/questior
Q SEARCH
Given the function is
f(x) = ln (1+x)
Step 2
Now
f(x) = ln (1 + x)
f'(x) = ₁⁄² x
1+x
ƒ” (x)
f" (x)
f""" (x)
f"'""" (x)
Step 3
=
Then
Rn (x)
Rn (x)
Rn (x)
=
ƒn (x)
fn+1(x)=
=
Rn (x)
|||
=
=
-
=
=
=
1
(1+x)²
2
(1+x)³
6
(1+x) 4
24
(1+x)5
(-1)^-¹(n-1)!
(1+x)"
ASK
=
(-1)^n!
(1+x)n+1
(-1)^n!
(1+g)n+1
(n+1)!
2!
(1+x)³
(1+x)³
fn + 1 (§)
· ( x
- §) n+1
(n+1)!
4!
(-1)^n!
(1+) n+¹ (n+1)n!
3!
(1+x)*
(-1)"n!
(1+ ε) n+¹ (n+1)
Vo))
LTE 1.1 LTE2 4+1 9%
+ [9]
(x − (− 1)) ¹+¹
·
√x MATH SOLV
(x + 1)^+1
(x + 1)n+¹
Transcribed Image Text:Let x = (−1,0) and let R₁(x) be the remainder in Maclaurin's formula for ln(1 + x) in Cauchy's form. Write down the formula for R₁(x). This
formula should contain three variables, n, x and, where = (x, 0).
R₁(x) =
=
Put On(x) = (1 + §)|x|¯¹|R₂(x)|. Based on the above formula for R₁(x), find the smallest constant a such that
Qn(x) ≤ alxn.
a =
Based on the above formula for Q(x), find the smallest constant b such that
|R₂(x)| ≤ b|x|¹+1
1-|x|*
b =
Evaluate
\x/n+1
limŋ→∞ T-|x|
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