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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[3]{1-x} \approx 1-\frac{1}{3} x$

$L(x)=1-\frac{1}{3}(x-a)=1-\frac{1}{3} x$(SEE GRAPH)we see from the graphs that for accuracy $y=0.1$ then $x$ must be $-1.204< x<0.706$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

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this question struck us, too. Determine the values of extra, which the linear approximation is accurate. First step is where we have acts. Cube root of one minus X plunk and zero solved. Then take the derivative off the cube drew of one minus X, where you have X again, plug in zero and we end up with simply negative 1/3 this term. Just become zero, Which means our l of acts is one minus 1/3 times X minus a which some funds to one minus 1/3 acts and we can see that X is accurate. If you are to look at the visual of this, it would be accurate between negative 1.2 of four and 0.70 sex.

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