Conner Ellis
05/07/2024 · Junior High School
\[ f(x)=\sqrt{10-x} \] Compare the values of \( \Delta y \) and \( d y \) if \( x \) changes from 1 to 1.07. (Round your answers to six decimal places.) \( \Delta y= \) \( d y= \) What if \( x \) changes from 1 to 1.02? (Round your answers to six decimal places.) \( \Delta y= \) \( d y= \) Does the approximation \( \Delta y \approx d y \) become better as \( \Delta x \) gets smaller? Yes No
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Quick Answer
When \( x \) changes from 1 to 1.07:
\[
\Delta y = -0.002000
\]
\[
d y = -0.0116667
\]
When \( x \) changes from 1 to 1.02:
\[
\Delta y = -0.006000
\]
\[
d y = -0.0033333
\]
Yes, the approximation \( \Delta y \approx d y \) becomes better as \( \Delta x \) gets smaller.
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