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

Chapter 3, Problem 29

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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?

\(f(x)=\sqrt{5-x}\)

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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?

\(f(x)=\sqrt{5-x}\)

ANSWER:

Step 1 of 3

For any function , the formula to find is  and the formula to find  is .

It is given that, when  and . Secondly, when  and .

                                 

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