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$7-10$ 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$
$L(x)=1-8(x-a)=1-8 x$for accuracy $y=0.1$ then $x$ must be $-0.045< x <0.055$
Calculus 1 / AB
Chapter 3
Derivatives
Section 8
Linear Approximations and Taylor Polynomials
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this question asks us to verify Gwen your approximation. The first step is where we have acts were going to plug and zero and solve. We get one now take the derivative so two times negative. For for the derivative, give us negative eight times 1/1 plus two x to the power five We're going to plug and zero for acts. Similarly, for what we did with the original function and soar, l've axe is gonna be one minus eight times X minus a which simplifies to one minus eight tons Axe. And then we know that if you are to draw a rough visual from us look something like this between negative 0.45 and 0.0
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