❖ Multivariable Calculus: Finding and Sketching the Domain ❖
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- Опубліковано 7 лют 2025
- Multivariable Calculus: Finding and Sketching the Domain of a function z = f(x,y).
In these examples, our domain will be some region D in the XY-plane. To find the region, we approach the problems much like when we have a function of a single variable.
Here I look at two examples of finding the domain and sketching the domain of a multivariable function. In particular we have a function of two variables.
#calculus #domain #multivariablecalculus
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I don't even listen to my teacher lecture. I just go straight to UA-cam and pray Patrick has a video on the topic.
dame true
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Kenny Huynh Hell yeah ..
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Been watching your videos since I was 12 taking algebra 1. 5 years later, I'm sitting in my college dorm, watching your videos taking multivariable calc. It's funny how some of your algebra videos are newer than your multivariable calc ones haha
i made calculus videos first :) then worked backwards
PatrickJMT you are AMAZING. You are my actual math instructor. Thank you so much. Please don't stop making these videos.
best maths teacher I've come across in my life
thank you sir....
happy to help :)
Thank you so much! Only took 3 minutes to clearly and concisely answer a question that I would have spent at least 20 trying to search for on my own.
patrickJMT is one of the main reasons why im getting through my calc series. Thanks again!
Andreajal986, the definition of range is the set of output values that is mapped to by the function after having some input value (the domain). In this case, the domain is the combination of x and y unknowns. Then by inputting it into function f(x,y), you get certain values. These values are the range of the function.
If you want to know some more, when patrick drawn the x,y,z axis system, the range is actually represented by the possible z values outputted from the function, with z = f(x,y).
The definition that range is the y-value only applies if it was a single variable function like f(x) = x^2 + 1, and y = f(x). But as this is multi-variable function, the range is no longer y-value.
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I appreciate that!
took 1 and half hour in class and still dont understand but from this video only took only 3 minute to understand it. thanks !
muhammad najib makes two of us
@@AndyB1993 That makes 3 of us. Did ya'll graduate already?
Great video, really good at teaching. I was feeling bad for not understanding this during the university lectures. But this video just help me understand everything.. short, easy, and straight to the point. Keep it up!
Thank You so much man, Tomorrow I have an exam, now I understand how to solve this.
Great work man! helped me sketch the domain of f(x,y) = ln(2x^2 + 2y^2 - 18) super easy, didn't even have to dig through the book.
Thanks man from 2022, you are helping me, i am from KZ, thanks a lot
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you saved me a world of trouble a few semesters ago with your calculus videos, always appreciated.
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I really hate working with domains for some reason, but you made it simple! Thank you!
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Best math teacher ever can you please make a video explaining the 3 dimensions and how to draw graphs/explain the tangents of sphere to different planes. my teacher was drawing scribbles on the board that didn't make sense. i ll really appreciate it
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Wow this is very good. Saved me from spending hours teaching it to myself.
Thank you for the good tutorials, I learn a lot of stuff in maths.Thumbs up and God bless you
Oh my god thank you so much I had a hard time understanding this during the lecture because my teacher isn t that good at explaining but you made it so simple thank you so much !
first vídeo and i already love you, Patrick!
Thanks for all your videos helped me so much for Calculus :)
You make things so simple.
Thank you so much. This was an amazing video on Multivariable
thank you for the help!
Great Work Sir 🔥
Excellent explanation!
Range defines all the y-values for the function. IMO for the 2nd example it should be y ≥ x^2, ergo all positive values of y.
Thank you, this was explained perfectly!! It's exactly what I needed. :D
Thanks for your videos.
Hi, I'm very grateful for your help and your dedication really you're the best!! Could you make at least 2 or 3 more examples? one of them including a circle equation pleaseee pleaseee!
Think you can explain how to find the range of a multivar function? Thanks again!
Awesome video. Thank you
In the second example, when graphing, you left out the radical, wouldn't it make a difference when graphing it?
If you want to find the range, you have any videos for that? With multivariables that is.
So what if the function was the squareroot of x*y. Since it's a root the domain means it has to be greater than zero. But then how do you solve for the equation to graph it? Would you just divide 0 by x and get y=0?
would xyz for example two just be a parabola projected diagonally from the x and y coordinated axes ? kind of like the first example, or is it too hard to think about?
can you do more example on Multivariable Calculus: Finding and Sketching the Domain
great videos patrick, always helpfull....but what about finding the range of a fxn of 2 variables?
for the denominator, isn't supposed to be 1+ x^2 not equals to 0???? rather than 1+ x^2 =0?
You are KING
Hey could you do some examples with more absolute value signs? I always have problems with those... Great job though!!
is it possible for you to do range of a multivariable function?
impressive video thanks brother
@citybutterfly26 i will keep making them : )
How would i take the domain of a function with sin or cos? For example like sin(x/y) please i really need help with this and im completely stuck
What should I do to find the Range of these functions. ??
Thank you for the video! it is helping a lot. just one question, on the first example, why is the domain above the line and not below it?
+Marcus Cowan Because the equation is y >= x^2 so the defined part of the function is above the parabola and not below it. hope that helps :)
That is a very interesting question
Can you do a video on how to find the range of a several value function? Use this equation: f(x,y) = 1+sqrt(9-y^2)
So what if I have a function f(x,y,z). How do I express the domain then?
What will be the range of second question??
you cant have a negative value inside the radical but you CAN have a zero inside of it. so, (-inf,0) is wrong. as long as both your x and y values are not negative, they can be any number or value they choose to be. so the domain would be (0,inf) for both x and y. D: {x,y| x ≥ 0, y ≥ 0}
It would be helpful if you could write out the domain at the end in the {f(x,y):.... form but video really helped thanks!
another great video!
Doesn't the natural log exist for both positive and negative values? But it just does not exist when it is equal to zero?
in the first example, why do you leave x alone and only solve for y?
For #2 could you also write the domain as 1-(x^2)>0? Or is it only correct to write it as numbers to exclude?
How can I sketch the domain of function in ex2 by using matlab ?
Thank god for you
This is best video
what book do you get the samples from
make videos of every possible problem of a book!! :)
2:10 Sketch
for the function f(x,y) = root(x) + root(y) why wouldn't it be from (-inf,0)U(0,inf)? If x>y then it's fair to not be 1? I'm confused with this question still and this video didn't really help with it :(
many thanks
Thank u so much sir
I think it should be shaded -1
Is the topic of domains learned in Calculus 1?
no, it is learned in a first course in algebra
THANK YOU SO MUCH
So one of the questions I was given was x^2y^2 / x^2y^2 + (x-y)^2 and if x^2y^2 >=0, how do I calculate the domain for the denominator? I am slightly confused, can you help me please?
i didnt get it, what is the domain? specially for the first one
How would you graph something like f(x,y) = y or f(x,y) = sinx? Thanks!
EX 1 WHY was the point (1,1) chosen????? cuz you cant use the origin as a test point with out knowing the lines crosses thru those points ???? WHY is no one at all mentioning this
thank u very much u helped me a lot
Thx, my lecture cannot let me understand efficiently, but you can.
thank you sir.
Shouldn't the y greater than or equal to x^2 domain be outside the parabola? Since it's greater than? I.e. a domain x^2 + y^2 greater than or equal to 9 would have all its points lie outside the circle
this is an old question but for other people: no, think of the parabola as having infinite length and then ask what is above and what is below this line. or ask yourself for any given x value on what side of this line are the y values greater.
hello,how to made the graph of two varable function?
the left handed god strikes again!
The devil's hand is upon us!
in second example it must be x not equal to -+1 ?
I'm having a hard time finding the domain and range of f(x,y)=e^(x*y)
How do I even separate the variables to find the domain and the range?
well, the domain of an exponential function is all real numbers; and its range is all numbers greater than zero. there is nothing that will make x or y undefined and their product is also defined. so the domain is all real numbers and the range is > 0
THANK.
YOU.
what is the range of this function?
This was incredibly helpful, thanks!
Thnx a lot, much appreciated
It's helpful thx a lot
How do I figure out the range?