text-if-lim-_x-rightarrow-4-fracfx-5x-21-text-find-lim-_x-rightarrow-4-fx

Question

$$	ext { If } \lim _{x ightarrow 4} \frac{f(x)-5}{x-2}=1, 	ext { find } \lim _{x ightarrow 4} f(x)$$

Amy Jiang · Accepted Answer

okay so as to find the limit as extra poaches for of So let&#x27;s start by using our quotient. So if we did that, we get the following with limits as experts four of FX and then we can use a different role here, sort of limits as X approaches 45 all over the limits as expertise. Four of X minus the limits as X approaches for of. So that&#x27;s all equal to one. So we have the limits as X approaches four of ffx minus the limit of a constant that just equal to a constant threats minus five over the limit as activities for four. That&#x27;s four minus. The constant to is you go to one. So yet this whole denominator is equal to two. We can multiply to on both sides, and we&#x27;ll get the limit as X, which is four of off of X minus five, is equal to two. Adding five to both sides We get that are limits is equal to seven

Carter Rogers · 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

So that&#x27;s all for this limit here will be first need to do is to find the inverse function right here. So in order to do that, we need to solve. You can swap the axis for wives. And this, my friend X to be a X is equal to two. Why plus read bye bye. Why plus four most by both sides. By why plus four You guys Thanks. Because what? Plus four with your sex y it&#x27;s for X is equal to why plus three that&#x27;s attracting both sides by two Why and also speckled signs before X. What we get is X Y minus two. Why is equal to three minus four Hex Proctor. Why here Me of why Times X minus two is three minus for X. So then, if we continue up here, divide both signs by X minus two. To get why is equal to three minus four X divided by X minus two. He was also actually equal to the inverse. How about the vex? So if we&#x27;re looking for the limit, his exit purchase five of the University of X, we know that the function will be to so far three minus four x x minus two So to solve for this limit now we can plug in 54 x to me of three minus four times five, divided by five minus two, which is vehicle to negative 17 divided part three.

Yaw Asomani · Answer

that is have this inequality? Uh, for X minus one over ice. Right in less than FX. Less than nursed in, uh, four x squared plus three x over X squared. So we wonder limits as X approaches infinity. Right. So let me ask. X approaches Infinity listing the limit as X approaches infinity off the left side. What is What is it? You divide it in a return by X right? Which is the highest, the XP, the highest power at the denominator. And then this becomes for minus one over X. Then this is Ah, one. Right. So as X approaches infinity, this is gonna go to zero. So this is gonna have 4/1, right? For of awareness is just four. So does this for now. Let&#x27;s consider the right hand side here. So what is the limit? Has X approaches infinity off the right hand side, right. Instead of same thing, we&#x27;re gonna gonna divide each and every turn by X squared here, right? When you do that, what is gonna happen is gonna be four minus three over X right, because when you divided by X squared, you have three over X. That is gonna be one so entered, a limit as except reaches infinity. This one is also going to be four, right? So the limit asked except reaches infinity of the left hand side is for And it&#x27;s the same thing for the limit as exactly this infinity of the right hand side. So by the squeeze theory or the sandwich rule than the limit as X approaches, infinity of the middle one is also gonna before.

Amy Jiang · Answer

Okay, so we want to find her following limits. So let&#x27;s start by using our Kocian role. Do you? Everything separate the following into two limits a limit as X approaches for of a flex all over the limits as experts for of Geo Vex So we can hear it This as 16/8. What is 16/8 have people to to

Amy Jiang · Answer

they&#x27;re so we want to find a falling limit. So it&#x27;s not that we have a question of two terms. So here we can use our question wrong. And then in our numerator, we have a some so we can use or some room on Dhere. We have a constant multiplied by our function within pool or limits just into our function. So it&#x27;s your at this as the limits as X approaches four of awful X plus the limits as X approaches for of geo vax. And this is all over two times the limits as X approaches for of job so we can replace our limit of us. Relax with 16 g of X with eight, this is all over two times eighth. So what? 16 plus eight? That&#x27;s equal to 24 all over two times eight. But you&#x27;re 16. So what&#x27;s 24/16? You see that this simplifies into a, um 3/2

Problem

If $\lim _{x \rightarrow-2} \frac{f(x)}{x^{2}}=1,…

Problem 79 Hard Difficulty

$$\text { If } \lim _{x \rightarrow 4} \frac{f(x)-5}{x-2}=1, \text { find } \lim _{x \rightarrow 4} f(x)$$

Answer

$$7$$

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Joel Hass, Christopher Heil, Przemyslaw Bogacki

University Calculus: Early Transcendentals

Grace H.

Anna Marie V.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$$7$$

University Calculus: Early Transcendentals

Grace H.

Anna Marie V.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Joel Hass, Christopher Heil, Przemyslaw BogackiUniversity Calculus: Early Transcendentals

Grace H.

Anna Marie V.

Kristen K.

Joseph L.

Joel Hass, Christopher Heil, Przemyslaw Bogacki

University Calculus: Early Transcendentals