French Ross
07/22/2023 · Middle 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? No Need Help?
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Quick Answer
- 当 \( x \) 从 1 变化到 1.07 时:
\[
\Delta y = -0.003
\]
\[
dy = 0.011667
\]
- 当 \( x \) 从 1 变化到 1.02 时:
\[
\Delta y = -0.006
\]
\[
dy = 0.003333
\]
- 随着 \( \Delta x \) 的减小,\( \Delta y \approx dy \) 的近似变得更好。
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