verify-the-given-linear-approximation-at-a0-then-determine-the-values-of-x-for-which-the-linear-ap-4

Question

Verify the given linear approximation at $a=0 .$ Then determine the values of $x$ for which the linear approximation is accurate to within $0.1 .$
$$1 /(1+2 x)^{4} \approx 1-8 x$$

Jack Chen · Accepted Answer

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&#x27;t forget we have a knowledge to in the end, which comes from the the co feature in the Randall Bex. It&#x27;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&#x27;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.

Jack Chen · Answer

for this program we want to find out of immunizations. So its first compute, um, the dura tiff off f by the terrible you&#x27;ll be this. So don&#x27;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&#x27;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.

Amrita Bhasin · Answer

okay. We know the four through of one plus two acts. Amino X zero gives us one there for the derivative would be 1/2 times one plus. If you plug in zero, we end up with 1/2. Therefore, we have the four through of one plus two. Axe equals one plus 1/2 axe. Therefore verifying this We know we have 0.1 is less than the four through of done pushed you axe on a swan. And this 1/2 acts, which is less than 0.1. Therefore we have 0.9 is less than four through of one plus two acts minus 1/2 axe. Just lost them 1.1. So we have. Why&#x27;s your 0.9? White is 1.1 to the values would be between the of 0.3689 and 0.6777

Amrita Bhasin · Answer

we know the first thing we&#x27;re gonna be doing is the natural log of one plus ear, which is just the natural above one which we know zero. Therefore, we know that the derivative is one over one plus acts. Now, remember, the natural log of one plus axe is equivalent to axe. So then, if we&#x27;re able to graft this, it would look something like this. And we know that X would be between negative 0.3832 and 0.5162

Amrita Bhasin · Answer

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&#x27;re going to plug and zero for acts. Similarly, for what we did with the original function and soar, l&#x27;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

Jack Chen · Answer

in this question. Um, wrong to figure out what Salim Iraq. Well, the very fires remilitarization of it is given by ice giving the, um, program. So for us, we need to figure out the directive we just given by this. So the view militarisation had X equals toe A, um yes. Given by half of a process of crime off a times X minus A in this case, a course zero. So we have the immunisation because the Y minus three x, which and you were verified. Um, the equation giving in the program is correct. And then we also want to figure out, um, within which interval the error between the demilitarization and a extra function. Yes, less than the opening one. That means we&#x27;re solving this in quickly on minus one. Right. Sorry. I should be the memorization minus. Um do you extra function so you can use the horrific calculated to find out this interval. So the interval used to ah is from minus 0.1162 to 0.14 full. One

Problem

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

Problem 9 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 $0.1 .$
$$1 /(1+2 x)^{4} \approx 1-8 x$$

Answer

$-0.045 < x < 0.055$

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James Stewart

Essential Calculus Early Transcendentals

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Anna Marie V.

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Joseph L.

Precalculus Review - Intro

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$-0.045 < x < 0.055$

Essential Calculus Early Transcendentals

Catherine R.

Anna Marie V.

Kayleah T.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartEssential Calculus Early Transcendentals

Catherine R.

Anna Marie V.

Kayleah T.

Joseph L.

James Stewart

Essential Calculus Early Transcendentals