Determining Independent and Dependent Variables in Calculus

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Discussion Overview

The discussion revolves around identifying independent and dependent variables in calculus, particularly in the context of functions and their interpretations. Participants explore how these terms apply to various scenarios, including geometric and practical examples.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how to determine which variable is independent or dependent, using the area of a circle and its radius as an example.
  • Another participant agrees that both variables can be viewed as dependent or independent depending on the perspective taken.
  • A participant cites a textbook definition of independent and dependent variables, suggesting that the definitions seem straightforward but can lead to confusion based on interpretation.
  • Concerns are raised about the usefulness of the definitions provided in the textbook, with one participant expressing skepticism about their clarity and relevance.

Areas of Agreement / Disagreement

Participants express differing views on the definitions of independent and dependent variables, with some agreeing that context matters in determining their roles, while others find the textbook definitions lacking in clarity.

Contextual Notes

There is an acknowledgment of the potential for confusion in interpreting which variable is independent or dependent based on the context of the problem. The discussion reflects a range of interpretations and assumptions about the definitions provided.

Who May Find This Useful

This discussion may be useful for students new to calculus or those seeking to understand the conceptual framework of functions and variable relationships.

crono_
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Calculus is quite new to me, so I think I'm starting from scratch and might be in over my head. Forgive my basic knowledge...

When considering two variables, how does one know which one is the independent or dependent variable?

For instance - The area A of a circle depends on the radius r of the circle.

Okay, it clearly states that A is dependent on r. But can you not also say that r is dependent on A?

If you have a bigger radius then you'll have a bigger area. But vice versa, if you have a bigger area than then don't you automatically get a bigger radius? Doesn't this mean that they can both be considered the dependent or independent variable depending on how you view the question?

Thank you!
 
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Hi crono_! :smile:
crono_ said:
When considering two variables, how does one know which one is the independent or dependent variable?
…
Doesn't this mean that they can both be considered the dependent or independent variable depending on how you view the question?

Yes!

You'll find soon that if y is a function of x, then you can differentiate and get dy/dx, but that's also 1/(dx/dy), the derivative of x as a function of y.

(btw, I'm not sure where you got "independent" or "dependent" from, for one variable … there's not much point in a variable unless something depends on it, is there? :wink: … of course, if there's two or more variables, they can be independent or dependent of each other)
 
Okay, thanks. That kind of helps to clear things up. Though I'm going to have to adjust to using calculus lingo. :)

The dependent & independent terms came from the textbook:

A symbol that represents an arbitrary number in the domain of a function f is called an independent variable.

A symbol that represents a number in the range of f is called a dependent variable.

That sort of seems straightforward, but my brain tells me that, depending on how you interpret the question, either of the two given variables could be dependent or independent.

The cost C of mailing a first-class letter depends on the weight w of the letter.

So, given the weight you can determine the cost. But, coming from the other direction, if you're given the cost then you can use that to determine the weight.

This is going to be a long term!
 
crono_ said:
The dependent & independent terms came from the textbook:

A symbol that represents an arbitrary number in the domain of a function f is called an independent variable.

A symbol that represents a number in the range of f is called a dependent variable.

Must say, that seems a bit daft to me. :confused:

And pointless. :rolleyes:

oh well …
 
tiny-tim said:
Must say, that seems a bit daft to me. :confused:

And pointless. :rolleyes:

oh well …

Comforting. haha :P

Well, thanks for the comments anyways. They're appreciated, and comical! :)
 

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