🟡01 - Functions of Several Variables (Domain and Range of a function)

In this lesson we are going to start a new course - Multivariable Calculus or Calculus 3
Functions of Several Variables: are functions that take multiple inputs (more than one input) to produce a single output or multiple outputs.
We shall in this lesson expose ourselves to functions of two or more variables and how to find the range and domain of such functions.
A function of two variables x and y may be presented in the form, z = f(x,y). And example is a function of two variables is the area of a rectangle, thus
A = l * w, then: A = f(l,w) = l * w
A function of three variables x, y and z may as well be presented in the form, w = f(x,y,z). And example is a function of three variables is the volume of a rectangular box, thus
V = l * w * h, then: V = f(l,w,h) = l * w * h
Domain: the set of ordered input values that produce a unique real value for the independent variable OR the set of ordered input values that makes the function defined.
Range: the set of output values of the function.
Playlists on various Course
1. Applied Electricity
• APPLIED ELECTRICITY
2. Linear Algebra / Math 151
• LINEAR ALGEBRA
3. Basic Mechanics
• BASIC MECHANICS / STATICS
4. Calculus with Analysis / Calculus 1 / Math 152
• CALCULUS WITH ANALYSIS...
5. Differential Equations / Math 251
• DIFFERENTIAL EQUATIONS
6. Electric Circuit Theory / Circuit Design
• ELECTRIC CIRCUIT THEOR...
7. Calculus with Several Variables
• CALCULUS WITH SEVERAL ...
Make sure to watch till the end.
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Thank you.

[@SkanCityAcademy_SirJohn]

9:00 - 10:32 The range of eg 1, ie. z = x^2 + y^2, is Z = [0, +inf) or z >=0 since any set of (x,y) will make z either 0 or a positive real number. Kindly take note.

[@EdisonvsTesla]

Nice

[@SkanCityAcademy_SirJohn]

@EdisonvsTesla thank you too

[@ibrahimabdulai8776]

Please I don't think it is from [0,+inf) because it is from the domain that we can get the range and the domain is a closed set at the positive side as 4 which means any two values of x and y when squared, added and the result is less than or equal to 4, those are the values of x and y which will give us the range of this function. Therefore, the range will also be restricted, the maximum number that can be produced in the range is 2. Is there a situation whereby the domain is a closed set at one end and the range becomes an open set at that same end please?

[@ibrahimabdulai8776]

I think it will only be [0,+inf) if the domain is also up to infinity

[@SkanCityAcademy_SirJohn]

@ibrahimabdulai8776 it mostly depends on the function in question....

[@ApochieIshmael]

Wow! indeed you are doing marvelous well in your delivery

[@SkanCityAcademy_SirJohn]

Thanks so so much...keep watching for more.

[@mathsetc.]

Nice informative video. One correction suggested. The range of z=x^2+y^2 is [0, Infinity) because of the squares and not the interval as shown in the video.

[@SkanCityAcademy_SirJohn]

Thanks so much for the correction, I really appreciate it.

[@nahomtesfaye5315]

you're good teacher thank you a lot

[@SkanCityAcademy_SirJohn]

You are most welcome. Thanks so much for watching as well.

[@DanielOluwafemi-xd2jy]

You are certainly Ghanaian! 😂
Enjoying you from Nigeria though!

[@SkanCityAcademy_SirJohn]

That's true😂😂😂 thanks so much.
Guess you've had some nice experience with ghanaians

[@user-ni9mt8oh1s]

Please try to make short videos too please… for quick understanding for test

[@SkanCityAcademy_SirJohn]

Noted with thanks

[@EdisonvsTesla]

ln(y-2x)≥0=y-2x ≥1
. And y-2x>0 . I think it has two solution, we can take their intersection, thanks in advance from Ethiopia 🇪🇹

[@SkanCityAcademy_SirJohn]

Zero cannot be part of the domain, because Ln(0) is undefined.

[@mhlengincama9809]

in 18:03 is'nt the range (-inf to 0)u(0 to 1) because 1 over something will always bring value less than 1?

[@SkanCityAcademy_SirJohn]

Yes, but then the main idea is that for 1/z + 1, which value of z will produce a define answer or value for x, and all values will do the except when z = 0.
Eg. When
z = 1, x = 2
z = 2, x = 1.5 and so on and on....

[@lesediphora3798]

please introduce Limits and Continuity

[@SkanCityAcademy_SirJohn]

Noted with thanks

[@kennedynyarko8063]

Keep it up bro

[@SkanCityAcademy_SirJohn]

Thank you very much

[@jamesowusuboakye4420]

Pls is the equation of line in 3 D

[@SkanCityAcademy_SirJohn]

Check the playlist link of several variables

[@longolongogoodson1285]

We want videos on ac circuits also Sir

[@SkanCityAcademy_SirJohn]

Please check the Applied Electricity playlist

[@SkanCityAcademy_SirJohn]

ruclips.net/p/PLInywrvFyvq7pFsDEDu2-n0f5UOhpqWBD

[@RRR_ACADEMY1]

Thank you Sir! I am from Sri Lanka! I am also conducting Educational youtube channel Sir☺

[@SkanCityAcademy_SirJohn]

Aww great. Good luck

[@RRR_ACADEMY1]

@@SkanCityAcademy_SirJohn Thank you so much my dear Sir!😊

[@SkanCityAcademy_SirJohn]

You are most welcome

[@jamesowusuboakye4420]

Pls the equation of a plane in 3 D

[@SkanCityAcademy_SirJohn]

Okay, check the playlist link for several variables, you will see it there.