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Numerade Educator

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Problem 31 Easy Difficulty

Explain, in terms of linear approximations or differentials, why the approximation is reasonable.
$ \frac {1}{9.98} \approx 0.1002 $

Answer

$f(9.98)=1 / 9.98 \approx 0.1-0.01(-0.02)=0.1+0.0002=0.1002$ so the approximation is reasonable.

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Video Transcript

we know that f of X is one over acts. Therefore, we know that after prime of 10 plugging into the derivative may have turned to the night of two, which is negative 0.1 Therefore, 9.98 would be 0.1 plus negative 0.1 times Negative. 0.2 is 0.1002