Calculus 3 help needed. confusing piecewise. I need explanation

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Homework Help Overview

The discussion revolves around understanding a piecewise function defined on the domain x ≥ 0; y ≥ 0. Participants express confusion regarding the notation and how to interpret the function's definition.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the meaning of the piecewise notation and how to apply the values given in different regions. There is an inquiry about how to find the domain and sketch the function based on the provided conditions.

Discussion Status

Some participants have offered guidance on interpreting the piecewise function and suggested drawing lines to visualize the regions defined by the function. There is an acknowledgment of confusion and a request for further hints, indicating an ongoing exploration of the topic.

Contextual Notes

Participants note that the notation is unfamiliar and that the problem was not covered in class, leading to additional uncertainty about how to approach it. There is mention of a specific part of the problem that was resolved with the help of a textbook.

bombz
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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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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" )
 
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.
 
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)
 
ahh that makes sense :) thank you so much!
 

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