Taylor series the taylor series generated by f(x) at x=a is .. f(a) F(a) f(a)+ (x - a) + (x-( f" (a) a)²+...... (x-a)n 1! 2! n! Example /find the taylor series for f(x)=cos x at x=2π. Soltion// f(x)cos x. ƒ(2π) = 1 f(x) = -sinx. F(2) = 0 F(x) = - COS X. F(2π) = =-1 The taylor series is 1 1+0- (x- -2)²+..... 2! Example/find the taylor series for f(x)= ½- at x=2. Soltion// 1 f(x) == ½ ½ ƒ(2) = 1 f(x) = 11. F(2) = 44 2 1 7(x) = 23. 7(2) = 1/13 - 11 = 8 4 The taylor series is 1 1 (x-2)+ 2 4 * 1! 4 * 2! 1 (x − 2)²+.....
Taylor series the taylor series generated by f(x) at x=a is .. f(a) F(a) f(a)+ (x - a) + (x-( f" (a) a)²+...... (x-a)n 1! 2! n! Example /find the taylor series for f(x)=cos x at x=2π. Soltion// f(x)cos x. ƒ(2π) = 1 f(x) = -sinx. F(2) = 0 F(x) = - COS X. F(2π) = =-1 The taylor series is 1 1+0- (x- -2)²+..... 2! Example/find the taylor series for f(x)= ½- at x=2. Soltion// 1 f(x) == ½ ½ ƒ(2) = 1 f(x) = 11. F(2) = 44 2 1 7(x) = 23. 7(2) = 1/13 - 11 = 8 4 The taylor series is 1 1 (x-2)+ 2 4 * 1! 4 * 2! 1 (x − 2)²+.....
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
Question
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![Taylor series
the taylor series generated by f(x) at x=a is ..
f(a)
F(a)
f(a)+
(x
-
a) +
(x-(
f" (a)
a)²+...... (x-a)n
1!
2!
n!
Example /find the taylor series for f(x)=cos x at x=2π.
Soltion//
f(x)cos x. ƒ(2π) = 1
f(x) = -sinx.
F(2) = 0
F(x)
= - COS X.
F(2π) =
=-1
The taylor series is
1
1+0-
(x- -2)²+.....
2!
Example/find the taylor series for f(x)= ½- at x=2.
Soltion//
1
f(x) == ½ ½ ƒ(2) = 1
f(x) = 11. F(2)
=
44
2 1
7(x) = 23. 7(2) = 1/13 - 11
=
8 4
The taylor series is
1
1
(x-2)+
2
4 * 1!
4 * 2!
1
(x − 2)²+.....](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9df3ff7-b32d-41ba-93f6-d46b6b6a8d9a%2F5e7e7d89-c70f-4f4a-9f9e-0919263bf175%2F9alffx6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Taylor series
the taylor series generated by f(x) at x=a is ..
f(a)
F(a)
f(a)+
(x
-
a) +
(x-(
f" (a)
a)²+...... (x-a)n
1!
2!
n!
Example /find the taylor series for f(x)=cos x at x=2π.
Soltion//
f(x)cos x. ƒ(2π) = 1
f(x) = -sinx.
F(2) = 0
F(x)
= - COS X.
F(2π) =
=-1
The taylor series is
1
1+0-
(x- -2)²+.....
2!
Example/find the taylor series for f(x)= ½- at x=2.
Soltion//
1
f(x) == ½ ½ ƒ(2) = 1
f(x) = 11. F(2)
=
44
2 1
7(x) = 23. 7(2) = 1/13 - 11
=
8 4
The taylor series is
1
1
(x-2)+
2
4 * 1!
4 * 2!
1
(x − 2)²+.....
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