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Numerade Educator

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Problem 7 Easy 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.
$ \ln (1 + x) \approx x $

Answer

$-0.3832<x<0.5162$

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Video Transcript

we know the first thing we're gonna be doing is the natural log of one plus ear, which is just the natural above one which we know zero. Therefore, we know that the derivative is one over one plus acts. Now, remember, the natural log of one plus axe is equivalent to axe. So then, if we're able to graft this, it would look something like this. And we know that X would be between negative 0.3832 and 0.5162