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Numerade Educator

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Problem 8 Medium Difficulty

Verify the given linear approximation at $ a = 0. $ Then determine the values of $ x $ for which the linear approximation is accurate to within 0.1.
$ (1 + x)^{-3} \approx -3x $

Answer

( SEE SOLUTION )

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Video Transcript

Okay, We know now that we have one plus x times. Negative three. This gives us one plus ax to the negative three, which is one minus three acts. Now we know that we can write this as night of 0.1 is less than one plus ax to the negative three. That's one plus three acts less than 0.1. So we know that if wise one plus extra negative three post reacts, then why's your 30.9 and 1.1? Therefore, we know the values for which approximation suffice spices would be negatives. Your 0.1162 is less than acts, which is less than 0.1441