Suppose I compute T₁(x), the degree 1 Taylor polynomial for f centered at x = 4. (a) Do you expect T₁(4.3) to be a good approximation to ƒ(4.3)? Explain why or why not. (b) Do you expect T₁(3.7) to be a good approximation to f(3.7)? Explain why or why not. (Hint: use a derivative of the appropriate order in your explanation.)
Suppose I compute T₁(x), the degree 1 Taylor polynomial for f centered at x = 4. (a) Do you expect T₁(4.3) to be a good approximation to ƒ(4.3)? Explain why or why not. (b) Do you expect T₁(3.7) to be a good approximation to f(3.7)? Explain why or why not. (Hint: use a derivative of the appropriate order in your explanation.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 51E
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Transcribed Image Text:A plot of the function f is shown below.
0.5
0
-0.5H
-1
L
-1.5
3.5 3.6 3.7 3.8 3.9
4
4.1 4.2 4.3 4.4 4.5
Suppose I compute T₁(x), the degree 1 Taylor polynomial for f centered at x = 4.
(a)
Do you expect T₁(4.3) to be a good approximation to ƒ(4.3)?
Explain why or why not.
(b)
Do you expect T₁(3.7) to be a good approximation to ƒ(3.7)?
Explain why or why not. (Hint: use a derivative of the appropriate order in your
explanation.)
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