suppose-that-lim-_x-y-rightarrow31-fx-y6-what-can-you-say-about-the-value-of-f31-what-if-f-is-cont-3

Name: suppose that lim _x y rightarrow31 fx y6 what can you say about the value of f31 what if f is cont 3
Uploaded: 2020-07-13
Duration: 2 min 42 s
Channel: Numerade
Description: Suppose that $\lim _{(x, y) \rightarrow(3,1)} f(x, y)=6 .$ What can you say about the value of $f(3,1) ?$ What if $f$ is continuous?

Question

Suppose that $\lim _{(x, y) \rightarrow(3,1)} f(x, y)=6 .$ What can you say about the value of $f(3,1) ?$ What if $f$ is continuous?

Julian Gerber · Accepted Answer

So let&#x27;s say we have a function in two variables f of X comma. Why and the limit of f of X comma y as X y approaches three comma one, um, is six. So what does that tell us about this function? Well, first we can say that s for long, equal to some devalue eso If we were to, um, plot this on a coordinate plain x y um, I&#x27;m not gonna show the Z axis because that&#x27;s ah free D. It&#x27;s a little harder to share in a drawing, but basically what this is saying is, if you have the 0.3 common one as, um as arbitrary points X y approach three comma, one from any and all direct, then the value approaches six. So as X comma y approaches three comma one, so does he approach six Bunch? If we were told, um, that f of X comma, why is continuous, um, at the point three comma one. Then you would be able to say not only does the approach sex, but Z equals six ep of X comma line rather f of three com. One equal six because that&#x27;s the ignition of continuity. If a function is consideration. I&#x27;m at a point. The and the and liver function at a poem is equal to, um, the limit of that, um, value at that point, um, so it&#x27;s continuous equal. Six. If it&#x27;s not us, we don&#x27;t know if it&#x27;s continuous or not. Then we can say f of x comma y approaches six.

Alan Ghazarians · Answer

is that we have this limit. What can we say about the value of F of three com one we don&#x27;t know, right? There could be, Ah, hole Or maybe and ask himto so we don&#x27;t know. But if F is continuous, then f a three common one is equal to six.

Jason Orozco · Answer

okay, were given that F is right continuous at X equals three. Which means that the limit as X goes to three from the right must be equal to the value of the function at X equals three. And we&#x27;re also given what that right limit is, which is f of X equal. Six. Uh, so we can just write her answer as people to six, and we can also ignore the extra given information of what you limit from the left is.

Brittany Knowlton · Answer

looking at this question, something that we know is that the function Excellent wine ice equal to three. And we want to see what we can say about the limit as ex wise approaching this point of f of x y and two different cases. First, about this continuous at this point, and secondly, if it is not continuous, so for suppose this continuous no, it&#x27;s not. Then clearly the limit as X Y goes Teo. Excellent wine. I&#x27;m if X Y is equal to three and we just know this from technicians and everything. If it&#x27;s continuous there, then clearly the limit will just equal to three. Since we&#x27;re playing in these points for X and Y. However, if if it&#x27;s not continuous, then we don&#x27;t really know much about the value of the function. At that point, when we were taking the limit, the limit I could have any value different from three not really just depends on the type of this continuity there, but if you have any value different from three or the limit may not even exist at that point,

Ahmed Ibrahim · Answer

from this question. If the function f is continuous at explode and why no, then our limit when X and y approaches x Nord and why don&#x27;t for function f x on why must equal to function off ex moat on why node, which is equal to three as government.

Agata Pavone · Answer

what let&#x27;s supposed to have two functions f n g off continues above continuous. And we also know that that&#x27;s why did Containers We also know that G job two is equal six and we know also that limit when X approaches to free Al Flex Plus in flex geo eggs equal 36 We want to know divine you effort to question Mark So what can we do? What we know that the two functions are continuous So we know that the limit when X purchase to the limit of our fullbacks is equal As to onda limit while X approaches to a t you fax is equal to yours too. This is because the two functions are continues. Dad, we know Geo, Do we want to know why? Foot, Let&#x27;s look at this limit whose value is known? Fact e six. So we have the limit off the sun off two functions. The 1st 1 is free of X and the 2nd 1 is the product off f of X to your backs. So we can say that the name is when except purchase to off free your backs plus have for Max to your ex equal This is, the sum often functions. The limit off the sun is equal to the sum off the limits On the product of a Kirsten, The limit off Causton times a function is equal by thinking about the properties of millions is equal to the constant times limit are the function and then the limit of Osama see equal to the son of the limits. And we also know that the Lear it on the product of two function is equal to the product off the to limits. Name it off the first function times. Name it when X approaches the same money to off the second function. So let&#x27;s see now. Now we know that the two functions f engineer continuous attack sequence to So we know that live it when x a purchase to over four backs. We know that is equal toe to Plus we know that limit off. Expect for when X separatists to of a fire effort taxes equal effort to guys and see you too. That&#x27;s because they&#x27;re two functions are continues and we also know that this name it the new German is equal to 56. So we can Blufgan divine you off you too. And so we have free after two laugh. What you have to is 662 Ikhwan fantasist eggs. It means free plus six is 9/2 of to equal. 36. It means effort to is equal for Oh, this is then the question is just what we were asked at the beginning. Find the value off I talked to.

Problem

Explain why each function is continuous or discon…

Problem 1 Easy Difficulty

Suppose that $\lim _{(x, y) \rightarrow(3,1)} f(x, y)=6 .$ What can you say about the value of $f(3,1) ?$ What if $f$ is continuous?

Answer

We can't say anything about the value of $f(3,1)$ because we don't know
whether $f$ is continuous at $(3,1)$ or not. However, if $f$ is continuous at
$(3,1),$ then $f(3,1)=6$ since the function value must equal to its limit if $f$
is continuous.

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We can't say anything about the value of $f(3,1)$ because we don't knowwhether $f$ is continuous at $(3,1)$ or not. However, if $f$ is continuous at$(3,1),$ then $f(3,1)=6$ since the function value must equal to its limit if $f$is continuous.

Essential Calculus Early Transcendentals

Lily A.

Anna Marie V.

Kayleah T.

Samuel H.

Vectors Intro

Vector Basics - Example 1

James StewartEssential Calculus Early Transcendentals

Lily A.

Anna Marie V.

Kayleah T.

Samuel H.

We can't say anything about the value of $f(3,1)$ because we don't know
whether $f$ is continuous at $(3,1)$ or not. However, if $f$ is continuous at
$(3,1),$ then $f(3,1)=6$ since the function value must equal to its limit if $f$
is continuous.

James Stewart

Essential Calculus Early Transcendentals