solve-the-given-problems-find-the-linearization-lx-of-the-function-fxsin-cos-x-for-api-2-3

Question

Solve the given problems.
Find the linearization $L(x)$ of the function $f(x)=\sin (\cos x)$ for $a=\pi / 2$

Edward Downes · Accepted Answer

Okay. In this problem we are asked for the liberalisation Halifax. This function at the point A. So in order to do this, we need a slope and a coordinate. We&#x27;ll start off with the coordinate so we know that X coordinate is paid over to In order to get the Y coordinate. We&#x27;re just going to compute f of fire over to. So this is sign co sign a pie of the tube. Co sign a pie of the tube. We should know that that is zero. So this turns into sino zero, which we also know zero. So I coordinate that this linear ization needs to go through is pi over two common zero. Okay, Now comes the job of finding the slope. We&#x27;ll call that m Okay, that&#x27;s going to come from the derivative. So we need F prime of X first. So the derivative of sine is co sign. Okay. And then we chain onto this, the derivative of the inside the derivative in a function derivative of coastline we know is negative sign. Okay? We want the slope at a value. So pi over two. So we substitute pi over two in here. Okay, I don&#x27;t need to worry too much about simplifying this down because we&#x27;re gonna get a value out of here. Co signed a pi over two. We know zero sine of pi over two. We know that&#x27;s one. Okay. So we&#x27;re gonna end up with co sign zero times negative one coastline of zero. We know is one. So we got one times negative one. Just negative one. Okay, now we conform uh linear ization L. Of X. Using the point slope form. So y minus Y. One equals M X minus X. One. This is what we just found as I am. That&#x27;s a slope. So why am I in a zero equals negative one. Explain this pie over to a little bit of simplification leads us to why you cause negative X was fired over two. And that is the equation of our linear ization of X.

Amrita Bhasin · Answer

this question asked us to find the Lanier ization of the function. The first step is to plug in a for axe when we get zero, then take the derivative. The derivative of co sign is negative Sign plug and A for ex again and now into the formula for linear or ization. We have us of a plus inverse function of or plus F promise acts. So that would be negative because we have a negative function. Times X minus a. This simplifies to negative acts, plus pi over to remember our power over two is our A.

Robert Daugherty · Answer

so section 3.9 We&#x27;re looking at problem number five everything in this section of dealing with linear ization. So using the first derivative to find a linear function that approximates are curved at a particular point. So we&#x27;re giving the function f of X equal the tangent of X and we&#x27;re interested in what linear function near is equal to pi will best approximate this function. So what, we&#x27;re gonna need to do this? We&#x27;ll need the the first derivative so f prime of X is going to be seeking squared of X. And so the linear function, the linear ization is going to be f of a plus f prime of a times X minus A and that will be a linear function that approximates are curved at the point x equal A So what is f of a So this is going to tell us that f l Love X is going to be equal to the tangent A pie plus and that&#x27;s gonna be the seeking squared of pie Times X minus. Hi. Okay, we know that the tangent of pie this is going to be zero, So l of X is equal to zero and the secret square to pie. That&#x27;s one over the co sign a pie. So this is going to be plus one over the co sign squared pi times X minus pi. The coastline of pie is negative. One you square that and you get one. So this all boils down to L. A vex equals X minus pi. So at the point x equal pie, This is a linear function that approximate our particular curve.

Linh Vu · Answer

Thanks, Coach. In a pension off x and my ankle to pry on it was asked to find a linear tradition X which has a formula ever I be coaching the temperament of a times X minus a so by sound of formula, we need to find a personal sorry And we need to find out if a on a prima a so ever buy we call Children have a good trip advisor about by here and they go to the attention of pie and touching. Look prime were called you zero and now we want to find an APRA. My so far since you find em crime. Thanks First coach you and attention of extended riff doomed attention in Coachella Swick and Square X and doesn&#x27;t implies that that every time the I would be a prima by with equal choda second square and a pie and we know that Can we go to one of ah course? I square under pry and cause I square on the buying when you go to one than for again of one here So we have the votes of the I am temperament may never on an X square Go Cheers! Oh bless one times x minus by ah go actually go to x minus by ondas We really answer

Amrita Bhasin · Answer

off of pi over six is sign of Pi over six, which is 1/2 therefore off. Prime of pi over six is co sign of power over six, which is three over to start squared off you over to there for the liberalization is gonna be 1/2 of a squirt of three over two terms Pai mei, which equal squared of three over two x minus pi over four squirt of three plus 1/2.

Jack Chen · Answer

for this question where you need to find out the tension line, which is also called The Memorization at X equals two pi over six. Um, we&#x27;re gonna use set up one phone. That is, if we&#x27;re given a function a four fix and we want to find out. Attend Unite X equals two a. By the slow point form, we have this formula y minus safe or very close to the purity. If at eight times X minus eight I&#x27;m saying this question is given and we need to figure out what say for Faye. I&#x27;m safe off a is Just sigh off high over six Now here we have and the f prime, the curative We will be, um, Costa fix So the narrative at X because they will be Kasai off higher the six now be Rudolph the Red Divide by two. With all this information we have why miners? 1/2 he caused to root off the red divide by two x minus piras six eso move this one have to the other side. So we have leg mineralization is given by kept in alof. X equals to route all three derived by two times x ah, minors. Um fruit off three pie divide by 12 and plus 1/2

Problem

Solve the given problems. Find the slope of a lin…

Problem 50 Easy Difficulty

Solve the given problems.
Find the linearization $L(x)$ of the function $f(x)=\sin (\cos x)$ for $a=\pi / 2$

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Precalculus Review - Intro

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus