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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Question
I need help with number 1. The table to use is attached.
![Power Series for Elementary Functions
Function
1
X
1
1 + x
=
1 (x - 1) + (x - 1)²(x - 1)³ + (x − 1)4 -
= 1 − x + x² − x³ + x4 – x³ + · · · + (−1)″ x" +...
In x = (x - 1)
et = 1 + x +
sin x = x -
cos x = 1
1
arctan x =t-
arcsin x = x+
3!
x²
2!
x3
3
+
記ざ
+
+
(x - 1)²
2
(1 + x)k = 1 + kx +
5!
+
5
x4
x6
4! 6!
-
x3
x4
+
x5
3! 4! 5!
+ +
1
+
+
7! 9!
7
+
x8
8!
+⁹
x3
1. 3x5
+
2.3 2.4.5
+
-
3
+
1)³
k(k
+
(x - 1)4
4
+
+
X"
+ +
n!
(-1)" x2n+1
(2n + 1)!
(-1)" x2n
(2n)!
1.3.5x7
2.4.6.7
k(k-1)x²
2!
*The convergence at x = ±1 depends on the value of k.
+... +
(-1)" x²n+1
2n + 1
+
1)(k − 2)x³
3!
-··· + (−1)" (x − 1)" +
+
+
+..
+
(-1)"-¹(x - 1)"
+...
n
(2n)!x²n+1
(2"n!)²(2n + 1)
+.
k(k − 1)(k − 2)(k − 3)x4
4!
+
+
Interval of
Convergence
0<x<2
-1<x< 1
0 < x≤2
-∞AXAM
-8AHA
T8AHA
-1≤x≤
-1≤x≤
-1<x<](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa098e07d-b15e-4284-9177-08ea985b9919%2Fd7e2f5ae-17f3-49ce-a17f-03d284fa8b23%2F0fwzvd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Power Series for Elementary Functions
Function
1
X
1
1 + x
=
1 (x - 1) + (x - 1)²(x - 1)³ + (x − 1)4 -
= 1 − x + x² − x³ + x4 – x³ + · · · + (−1)″ x" +...
In x = (x - 1)
et = 1 + x +
sin x = x -
cos x = 1
1
arctan x =t-
arcsin x = x+
3!
x²
2!
x3
3
+
記ざ
+
+
(x - 1)²
2
(1 + x)k = 1 + kx +
5!
+
5
x4
x6
4! 6!
-
x3
x4
+
x5
3! 4! 5!
+ +
1
+
+
7! 9!
7
+
x8
8!
+⁹
x3
1. 3x5
+
2.3 2.4.5
+
-
3
+
1)³
k(k
+
(x - 1)4
4
+
+
X"
+ +
n!
(-1)" x2n+1
(2n + 1)!
(-1)" x2n
(2n)!
1.3.5x7
2.4.6.7
k(k-1)x²
2!
*The convergence at x = ±1 depends on the value of k.
+... +
(-1)" x²n+1
2n + 1
+
1)(k − 2)x³
3!
-··· + (−1)" (x − 1)" +
+
+
+..
+
(-1)"-¹(x - 1)"
+...
n
(2n)!x²n+1
(2"n!)²(2n + 1)
+.
k(k − 1)(k − 2)(k − 3)x4
4!
+
+
Interval of
Convergence
0<x<2
-1<x< 1
0 < x≤2
-∞AXAM
-8AHA
T8AHA
-1≤x≤
-1≤x≤
-1<x<
![n
2
3
4
5
1. Find the nth Taylor polynomial centered at the given c. Use the included table to show work.
a. f(x)=e*,n=4,c=0
n!
P₁(x) =
f(") (x)
f(") (c) (x-c)"
f(n) (c) (x-c)"
n!
2. Using the attached table of Power Functions, find the power function for the given functions
and integrate the first 3 terms.
s(x)=e* sinx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa098e07d-b15e-4284-9177-08ea985b9919%2Fd7e2f5ae-17f3-49ce-a17f-03d284fa8b23%2Fbnb859_processed.jpeg&w=3840&q=75)
Transcribed Image Text:n
2
3
4
5
1. Find the nth Taylor polynomial centered at the given c. Use the included table to show work.
a. f(x)=e*,n=4,c=0
n!
P₁(x) =
f(") (x)
f(") (c) (x-c)"
f(n) (c) (x-c)"
n!
2. Using the attached table of Power Functions, find the power function for the given functions
and integrate the first 3 terms.
s(x)=e* sinx
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