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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 .$$$1 /(1+2 x)^{4} \approx 1-8 x$$

$-0.045 < x < 0.055$

Calculus 1 / AB

Chapter 2

DERIVATIVES

Section 8

Linear Approximations and Differentials

Derivatives

Differentiation

Applications of the Derivative

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in this question. We want to find out a living organization for if, um so. First, we need to find out that purity and the by the general We have the purity if he caused to this. So don't forget we have a knowledge to in the end, which comes from the the co feature in the Randall Bex. It's minus eight one cross to extend minus fact. And the immunization is given by hands off a plus if prime of a times X minus eight and in this case, a cause of zero. So we have one class so it's minus eight x to this day sitting notarization. And then we want to know within which interval on the era between the demilitarization and the ex extra function. Um, yes, bombing by their 0.1. So just plugging this toe functions So immunization minus one class two X to the minus four, which is the extra function so you can self the spy graphic calculator. So in the end we have the interval from 0.0 for five to positive 0.55 So this is the final result. So within this interval, whenever you choose X With the missing Hubble, the era between of immunization the F is strictly lessens your 0.1 that means this approximation is really good.

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