?Compare the values of \(\Delta y\) and dy if \(x\) changes from \(1\) to \(1.05\). What

Chapter 3, Problem 30

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QUESTION:

Compare the values of \(\Delta y\) and dy if \(x\) changes from \(1\) to \(1.05\). What if \(x\) changes from \(1\) to \(1.01\)? Does the approximation \(\Delta y \approx d y\) become better as \(\Delta x\) gets smaller?

\(f(x)=\frac{1}{x^{2}+1}\)

Equation Transcription:

Text Transcription:

delta y

x

1

1.05

1.01

Delta y approx  dy

Delta x

f(x) = 1/x^2 + 1

Questions & Answers

QUESTION:

Compare the values of \(\Delta y\) and dy if \(x\) changes from \(1\) to \(1.05\). What if \(x\) changes from \(1\) to \(1.01\)? Does the approximation \(\Delta y \approx d y\) become better as \(\Delta x\) gets smaller?

\(f(x)=\frac{1}{x^{2}+1}\)

Equation Transcription:

Text Transcription:

delta y

x

1

1.05

1.01

Delta y approx  dy

Delta x

f(x) = 1/x^2 + 1

ANSWER:

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