Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(4x) Σ 00 n = 0 Need Help? Read It

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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Use a Maclaurin series in this table to obtain the Maclaurin series for the given function.
f(x) = x cos(4x)
n = 0
Need Help?
Read It
Transcribed Image Text:Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(4x) n = 0 Need Help? Read It
E(-1)*---
1
E x" = 1 + x + x² + x³ + •
R = 1
1 - x
n=0
x²
x"
1 +
e*
R = 00
1!
2!
3!
n=0 n!
x3
x7
+
7!
x2n+1
sin x =
R = 00
(2n + 1)!
3!
5!
n=0
x²
x*
x°
E(-1)"
(2n)!
R = 00
2!
4!
6!
n=0
2n+1
tan¯'x = E(-1)" -
x'
+
7
-= x
R = 1
2n + 1
3
x3
x?
= X –
2
x*
+
4
In(1 + x) = E(–1)"-1
R = 1
3
n=1
k
x" = 1 + kx +
k(k – 1) 2 , k(k – 1)(k – 2)
|
|
(1 + x)* = £
x² +
2!
R = 1
3!
n-0
|
+
|
Transcribed Image Text:E(-1)*--- 1 E x" = 1 + x + x² + x³ + • R = 1 1 - x n=0 x² x" 1 + e* R = 00 1! 2! 3! n=0 n! x3 x7 + 7! x2n+1 sin x = R = 00 (2n + 1)! 3! 5! n=0 x² x* x° E(-1)" (2n)! R = 00 2! 4! 6! n=0 2n+1 tan¯'x = E(-1)" - x' + 7 -= x R = 1 2n + 1 3 x3 x? = X – 2 x* + 4 In(1 + x) = E(–1)"-1 R = 1 3 n=1 k x" = 1 + kx + k(k – 1) 2 , k(k – 1)(k – 2) | | (1 + x)* = £ x² + 2! R = 1 3! n-0 | + |
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