verify-the-given-linear-approximation-at-a0-then-determine-the-values-of-x-for-which-the-linear-ap-5

Question

Verify the given linear approximation at $a=0 .$ Then determine the values of $x$ for which the linear approximation is accurate to within $0.1 .$
$$(1+x)^{-3} \approx 1-3 x$$

Jack Chen · Accepted 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

Amrita Bhasin · Answer

Okay, We know now that we have one plus x times. Negative three. This gives us one plus ax to the negative three, which is one minus three acts. Now we know that we can write this as night of 0.1 is less than one plus ax to the negative three. That&#x27;s one plus three acts less than 0.1. So we know that if wise one plus extra negative three post reacts, then why&#x27;s your 30.9 and 1.1? Therefore, we know the values for which approximation suffice spices would be negatives. Your 0.1162 is less than acts, which is less than 0.1441

Amrita Bhasin · Answer

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.

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

Jack Chen · 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.

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

Problem

Use a linear approximation (or differentials) to …

Problem 10 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 $0.1 .$
$$(1+x)^{-3} \approx 1-3 x$$

Answer

$-0.1162 < x < 0.1441$

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$-0.1162 < x < 0.1441$

Essential Calculus Early Transcendentals

Catherine R.

Heather Z.

Kristen K.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartEssential Calculus Early Transcendentals

Catherine R.

Heather Z.

Kristen K.

Samuel H.

James Stewart

Essential Calculus Early Transcendentals