if-lim-_x-rightarrow-1-fx4-find-lim-_x-rightarrow-1-fleftx2right

Name: if lim _x rightarrow 1 fx4 find lim _x rightarrow 1 fleftx2right
Uploaded: 2020-06-20
Duration: 43 s
Channel: Numerade
Description: If $\lim _{x \rightarrow 1} f(x)=4,$ find $\lim _{x \rightarrow-1} f\left(x^{2}\right)$.

Question

If $\lim _{x \rightarrow 1} f(x)=4,$ find $\lim _{x \rightarrow-1} f\left(x^{2}\right)$.

Carter Rogers · Accepted Answer

So for this question, were given the information that the limit as exit purchase one of some function f of X is equal before. And then we&#x27;re being asked to evaluate that limit as X approaches. Negative one of f of X squared. We&#x27;ll go ahead and plug in that value of negative one so f of negative. One squared now negative one squared. We know that that&#x27;s just one. Some were given F one, and we know f of one from over here is four. Because the limit as X approaches one of f of X is for so we know that this is just for

Elizabeth Xu · Answer

different the limit as X approaches for of the inverse motion of vacuum packs. We first need to do this to find the inverse function of effort back. So what this eagles don&#x27;t So we know to find the interest of a function when we need to do is stop out these access for wise and the wife rednecks. So we have. Action is equal to two. Why close? One divided by why minus one. Help you multiply both signs by why minus one X Why Maya&#x27;s X is equal to two i plus one. And now we must solve for y to be of X y every. Subtract two from both sides and add extra boat signs. Get this. We have tractor out. Why cool one plus specs to redivide both sides. Pie X minus two will get his Why is equal to one plus X, divided by X minus two. Now this function is actually equal to the inverse of aftereffects. So if we&#x27;re looking for the limit, his actual purchase for of the inverse of ethics, which is one plus sex over X minus two but we can do is supply in four into this function for X. When we got one first four divided by four minus two is equal to five, divided by two

Elizabeth Xu · Answer

So we want to find a limit as X approaches eight of the inverse of active axe you first need to find with the inverse of a vest of f of X is equal to. So to do that, what we need to do is take this function here and swap out the F of X with the ex. So it&#x27;ll look something like that. Max is equal f of x squared plus four and now we solve for after effects. So we have subtracting both sides before you X minus for is equal to half of X squared. Indescribable signs will know that I have of X is equal to the square root of X minus four. In reality, what we just found is the inverse of a thanks. So if now we have the inverse it affects and we are looking for the limit as extra purchase eight become plugging a for bex. We&#x27;ll get square root of eight minus four, which is equal to screw before equals two

Alex Johnson · Answer

in this problem, we have the information that the limit is X goes to negative. Four of f of X is equal the three and we have the limit as X goes to negative four g of X is equal the one we&#x27;re trying to calculate the limit as X goes to negative four of f of X multiplied by G of X and the product Law of limits tells us that this limit could be simplified into the limit is exposed negative four of aftereffects multiplied by the limit as X goes to negative four of G of x, and this will give us three times one, which is three.

Madi Sousa · Answer

in this problem, we are given a limit that has a solution. We know the solution, and from there we need to figure out the solution to two other limits. So, really, what we&#x27;re dealing with here is beginning to understand how we can use limits across products and quotients of functions. And we&#x27;re going to be talking about that. If you&#x27;re cute, pardon me. If you&#x27;re confused now, hopefully this will make sense at the end of the video. So let&#x27;s first start out with what we&#x27;re given. Were given the limit as X approaches zero of ffx over X squared, and we know this limit is one. So for part A is saying, Well, let&#x27;s try to find the limit Is X approaches zero of f of X. This is not the same as the limit before, but can I find this limit knowing that the first one equals one? And the answer is yes, we can. The first thing that we&#x27;re going to do is will distribute this limit in the numerator and the denominator of are given function, so we&#x27;ll get the limit as X approaches zero of ffx divided by the limit as X approaches zero of X squared, and we know this equals one. So clearly we can see that if our exes approaching zero, our denominator is going to approach zero Aziz. Well, what zero squared? Well, that&#x27;s simply zero. So if we rearrange this, we would say the limit as X approaches zero of f FX equals one time zero. We just moved this denominator to the other side so clearly we can see that the limit is X approaches. Zero of F of X is zero, and now on to part B. Part B is a very similar procedure. But now we&#x27;re asked, Well, can we find the limit as X approaches zero of ffx over X? Well, yes. And now here&#x27;s we&#x27;re going to be learning how to do that product in quotient more rigorously. So we can say if we rearrange the original limit that it&#x27;s equal to the limit as X approaches zero of ffx over x times the limit as X approaches zero of one over X and we know that equals one because you can see if we multiplied these inter functions, we would get the function we started with so we could do a little bit of rearrangement on this second limit here will distribute that limit again, as we did before. So we&#x27;ll get this is equal to the limit as X approaches zero of f of X over X times the limit is X approach zero of one over the limit as X approaches zero of X. You know, this is still equal toe one. Well, again, we can use our intuition here. We can see that if X approaching zero, this denominator here is going to be zero as well. So what does that mean? That means that this is going to be zero is well, this entire term. If we take anything and divided by zero, we get zero. So if we know that this is zero, we could move it on to the other side. We can say the limit is X approaches zero of f of X over X right. This side equals one time zero. So we can say the limit as X approaches zero of f of X over X equals zero, which is what we wanted to find. So in this case, we found that both of the limits who were looking for R zero that is just a special case that we dealt with here. That&#x27;s not going to happen every time. So I hope that this problem helped you understand how we can start manipulating limits, using our knowledge of products and questions, and, specifically, how we can rearrange those functions to find two limits if we&#x27;re given one.

Jade Meyer · Answer

given that the limit of the function F Lexx as except culture&#x27;s negative for is equal to three were also given that the limit of Kiev X as X approaches negative for is equal to one and were asked to find the limit of two times Ethel necks plus three times she vex as X approaches negative for Well. To do this, we can use the basic limit laws. The first law we can use is the somewhat So we can actually separate this into the limit of two times f of X as X approaches negative for times Sorry. Plus the limit of three times g vex as X approaches negative for we can actually simplify this even further by using the constant multiple law So we can change this into two times the limit of Ethel Axe as ex approach is negative for plus and we do the same thing for this limit. So we get three times the limit of chief ex as X approaches negative for and now all we have to do is plug in values. We know that the limit of f of X as X approaches negative forces equals three, so we can change this to two times three and we know that the limit of G of X as X approaches negative four equals one. So we can change us two plus three times one. This equals six plus three, which equals nine. So nine is our answer.

Problem

Suppose $g(x)=f(1-x)$ for all $x, \lim _{x \right…

Problem 104 Medium Difficulty

If $\lim _{x \rightarrow 1} f(x)=4,$ find $\lim _{x \rightarrow-1} f\left(x^{2}\right)$.

Answer

Related Courses

Calculus Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace H.

Catherine R.

Samuel H.

Michael J.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 2

Video Transcript

William Briggs, Lyle Cochran, Bernard Gillet

Calculus Early Transcendentals

Grace H.

Catherine R.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Calculus Early Transcendentals

Grace H.

Catherine R.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

William Briggs, Lyle Cochran, Bernard GilletCalculus Early Transcendentals

Grace H.

Catherine R.

Samuel H.

Michael J.

William Briggs, Lyle Cochran, Bernard Gillet

Calculus Early Transcendentals