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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.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.)
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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