Calculus 3 help needed. confusing piecewise. I need explanation

In summary, the conversation discusses defining a function in a two-dimensional step-function form for a given domain. The function is defined using the given values and the domain is the entire x,y plane. The participant also receives hints on how to approach the problem and how to sketch the function.
  • #1
bombz
10
0

Homework Statement



2. On the domain x [tex]\geq[/tex] 0; y [tex]\geq[/tex] 0, dene the function f(x; y) such that

[PLAIN]http://img100.imageshack.us/img100/2144/huhh.jpg

Homework Equations



I'm not so sure.

The Attempt at a Solution



I apologize for no attempt. I am just totally confused with this notation as I have never seen it before. What do I do with this?
 
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  • #2
hi bombz! :smile:
bombz said:
I am just totally confused with this notation as I have never seen it before. What do I do with this?

it means that you use the value given (0 1 or -1) for just the area given …

it's a sort of two-dimensional step-function :wink:

(and when it says "define the function", that's badly worded, it's not asking you to do something, it means "the function is defined this way" )
 
  • #3
Dear tiny-tim, how would I use those values then?

So basically,
This isn't a form we are using in class but from the piecewise, I am getting?
f(x,y) = 0 when x+1<y or when y <= x-1

How would I use that to find the domain though?? how would I even sketch it??

Sigh. Any more hints would be greatly appreciated. Part b I figured out with the book. Part a is what my teacher was so cool and added in when he never taught us something like this. I tried asking for help from friends but no one can figure out a.
 
  • #4
hi bombz! :wink:

draw the lines y = x - 1, y = x, and y = x + 1

write the value of f in each region between the lines :smile:

(the domain is the whole x,y plane)
 
  • #5
ahh that makes sense :) thank you so much!
 

What is Calculus 3?

Calculus 3 is the third course in the calculus sequence, also known as multivariable calculus. It covers topics such as vector-valued functions, partial derivatives, multiple integrals, and vector calculus.

What is a piecewise function?

A piecewise function is a function that is defined by different equations on different intervals of its domain. This allows for different rules or expressions to be used for different parts of the function.

Why is calculus 3 confusing?

Calculus 3 can be confusing because it introduces new concepts such as multivariable functions and vector calculus, which can be difficult to visualize and understand. It also builds upon the concepts learned in Calculus 1 and 2, so a strong foundation in those courses is important.

How can I get help with Calculus 3?

You can get help with Calculus 3 by attending office hours, forming a study group with classmates, or seeking help from a tutor. There are also many online resources and practice problems available to help improve your understanding of the material.

Can you explain piecewise functions?

A piecewise function is a function that is defined by multiple equations on different intervals. To evaluate a piecewise function, you must determine which equation to use based on the given input. This is typically done by setting up a piecewise function as a set of conditional statements and evaluating each condition separately.

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