Problem

Verify the given linear approximation at $a=0 .$ …

01:45

Problem 8 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 $0.1 .$
$$\tan x=x$$

Answer

$-0.631 < x < 0.631$

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Calculus 1 / AB

Essential Calculus Early Transcendentals

Chapter 2

DERIVATIVES

Section 8

Linear Approximations and Differentials

Discussion

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Video Transcript

in this problem won't go find demilitarization. Look for if, um so first we need to figure out the narrative. So with prime, Because to Seacon Square. So the militarization is defined by if off a plus f prime of a times X minus a in this case, eight because of zero. So we have zero plus x, which is just X. So So the memorization is given by a low X equals backs and then we want to know, um, were we want to know Come for which interval the Arab Tim, the demilitarization and the extra function If off x it's funded by zero queen one. So it project militarization. We have ex miners the actual function tenure next less than 0.1. So you you may use the calculator to derive the result. So the final interview is Rome. Mind still 0.631 to, um, hold here their 0.631 so basically, this in quality gives us too, um, Tween qualities. So the first vice X minus 10 Genetics This lesson there 0.1 The second wise X minus 10 year necks. It's great. Hidden for its greater the minus the appointments or just self this too, including cases when we have this interval. So within this interval, the era between eliminar ization and re extra extra hot and the function F is at most 0.1.

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