4.8 Taylor polynomials the taylor polynomials generated by f(x) at x=0 is .. F(0) fn(x) = f(0) + ƒ(0) -x+ 1! -x² +...... fn(0) -xn 2! n! Example //find the taylor polynomials generated by f(x)=ex at x = 0 soltion// f(x) = ex. f(0) = eº = 1 f(x) = ex. F(0) = 1 F(x) = ex. 7(0) = 1 The taylor poly. is 1 1 1 1! 2! +. -xn n! fn(x) =1+=x+ Example//find the taylor polynomials for f(x)= cos x. Soltion// f(x)cos x. f(0) = 1 f(x) = -sinx. F(0) = 0 F(x) == COS X. F(0) = -1 The taylor poly. is fn(x) = 1+0-12x²+.....
4.8 Taylor polynomials the taylor polynomials generated by f(x) at x=0 is .. F(0) fn(x) = f(0) + ƒ(0) -x+ 1! -x² +...... fn(0) -xn 2! n! Example //find the taylor polynomials generated by f(x)=ex at x = 0 soltion// f(x) = ex. f(0) = eº = 1 f(x) = ex. F(0) = 1 F(x) = ex. 7(0) = 1 The taylor poly. is 1 1 1 1! 2! +. -xn n! fn(x) =1+=x+ Example//find the taylor polynomials for f(x)= cos x. Soltion// f(x)cos x. f(0) = 1 f(x) = -sinx. F(0) = 0 F(x) == COS X. F(0) = -1 The taylor poly. is fn(x) = 1+0-12x²+.....
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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![4.8 Taylor polynomials
the taylor polynomials generated by f(x) at x=0 is ..
F(0)
fn(x) = f(0) +
ƒ(0)
-x+
1!
-x² +......
fn(0)
-xn
2!
n!
Example //find the taylor polynomials generated by
f(x)=ex at x = 0
soltion//
f(x) = ex. f(0) = eº = 1
f(x) = ex.
F(0) = 1
F(x) = ex. 7(0) = 1
The taylor poly. is
1
1
1
1! 2!
+.
-xn
n!
fn(x) =1+=x+
Example//find the taylor polynomials for f(x)= cos x.
Soltion//
f(x)cos x. f(0) = 1
f(x) = -sinx.
F(0) = 0
F(x)
== COS X.
F(0) = -1
The taylor poly. is
fn(x) = 1+0-12x²+.....](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9df3ff7-b32d-41ba-93f6-d46b6b6a8d9a%2F19307b7a-af33-49b8-b3a3-7d911a7143d5%2Fztgjlcg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4.8 Taylor polynomials
the taylor polynomials generated by f(x) at x=0 is ..
F(0)
fn(x) = f(0) +
ƒ(0)
-x+
1!
-x² +......
fn(0)
-xn
2!
n!
Example //find the taylor polynomials generated by
f(x)=ex at x = 0
soltion//
f(x) = ex. f(0) = eº = 1
f(x) = ex.
F(0) = 1
F(x) = ex. 7(0) = 1
The taylor poly. is
1
1
1
1! 2!
+.
-xn
n!
fn(x) =1+=x+
Example//find the taylor polynomials for f(x)= cos x.
Soltion//
f(x)cos x. f(0) = 1
f(x) = -sinx.
F(0) = 0
F(x)
== COS X.
F(0) = -1
The taylor poly. is
fn(x) = 1+0-12x²+.....
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