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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 .$$$\sqrt[4]{1+2 x}=1+\frac{1}{2} x$$

$-0.369 < x < 0.678$

Calculus 1 / AB

Chapter 2

DERIVATIVES

Section 8

Linear Approximations and Differentials

Derivatives

Differentiation

Applications of the Derivative

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for this program we want to find out of immunizations. So its first compute, um, the dura tiff off f by the terrible you'll be this. So don't forget, we have, ah to In the end, he comes for own the Corey featuring the crown topics. So in the end of the half, 1/2 when pressed to x to the miners three or four suddenly immunizations defined pipe um l o X equals stave off a process of prime of a hand six minus ending in this case equals zero. So we have one plus, so he should be one plus 1/2 X and that we want to know, um, on which interval this linear approximation is has a currency, uh, within 0.1. So basically, that means we want to solve this, um, in quality. And the result for this equality will be a internal eso. This means the ah of So tell you era off the picture. So this is the, um, extra value, and this is the approximation. So when we want tobe found this Arab by 0.1 so you can use our calculator to solve this equality, and that gives you an integral from minors. A 0.3 69 to, um, 0.678 Um, you know, to derive this result, basically, we are so being two different equations, the first wise, um, this whole thing's this air of because it was their 0.1, the otherwise the era you close to minus 0.1 and then we have this to balance.

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