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Numerade Educator

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Problem 25 Easy Difficulty

Use a linear approximation (or differentials) to estimate the given number.
$ \sqrt [3]{1001} $

Answer

$\sqrt[3]{1001}=f(1001) \approx f(1000)+d y=10+\frac{1}{200}=10.00 \overline{3} \approx 10.003$

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Video Transcript

we know that half of axes The cube root of ax Therefore, after prime of axe is 1/3. Remember the explain. It comes down to be the new coefficient times axe to the negative two divided by three, which is equivalent to X to the 1/3. Remember, we don't want any negative experiments over three acts. Cooking in 1002 the 1/3 over 3003 times 4000 gives us 10 over 3000 a one over 300. So now we have the cube root of 1001 is approximately 10 plus one over 300 which is equivalent to 300 Juan over 300.