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Problem 10 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.
$ e^x \cos x \approx 1 + x $
Answer
$-0.76 < x < 0.6$
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Video Transcript
we know that f of X is e to the X coastline exploding in 0 to 0 co sign zero anything to zero powers once. This is one times coastlines here, which is one. Therefore, the derivative is either the ex co sign X minus you the axe sign ex plug n zero and we end up with one. Therefore, we have each of the AKs. Co sign of acts is equivalent to approximately one plus acts. Now we know that we have negative 0.1 is less than either the axe co sign axe minus X minus one, which is less than 0.1. And we know 0.9 is less than either the axe co sign X minus fax, which is less than 1.1. So now, if we are to Graff, thus negative 0.763 is less than acts, which is less than 0.6 year of seven juice. It's between these two values
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