Predicting Asymptotic Relationship vs Linear

[dnovikov]

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So I pretty much always narrow down a question that asks about the relationship of two variables to the graphs that show the correct correlation except for one is asymptotic and one is linear... However I always seem to pick the wrong one. Whats the general rule from predicting the graph from a formula. Take for example this problem in Physics Book 2 section 8 on electrostatics and electormagnetism:

Why is it asymptotic and NOT linear...? Any help is greatly appreciated.

 

[MedPR]

So I pretty much always narrow down a question that asks about the relationship of two variables to the graphs that show the correct correlation except for one is asymptotic and one is linear... However I always seem to pick the wrong one. Whats the general rule from predicting the graph from a formula. Take for example this problem in Physics Book 2 section 8 on electrostatics and electormagnetism:

Why is it asymptotic and NOT linear...? Any help is greatly appreciated.

Linear is only for direct proportionality. So A proportional to (-B)
However, in this case the relationship is A is proportional to 1/B

You can study graphs, learn from experience, make up a few numbers, etc.

 

[milski]

AB=const is inversely proportional or asymptotic as you said
A/B=const or A=B*const is linear.

 

[SaintJude]

AB=const is inversely proportional or asymptotic as you said
A/B=const or A=B*const is linear.

Wow Kaplan had this exact same problem--I actually posted it. Apparently, very common mistake to confuse A & B, so it's a popular question.

 

[milski]

Wow Kaplan had this exact same problem--I actually posted it. Apparently, very common mistake to confuse A & B, so it's a popular question.

The graphs did look quite familiar. And I've seen the proportional/inversely proportional distinction brought up before.

 

[dmf2682]

Take the limit as your independent variable approaches 0 or infinity.

 

[dnovikov]

If its not too much to ask can anyone give an example of an asymptotic relationship using one general MCAT equation and a linear with another? It would make it a lot easier to understand. Thanks!

 

[milski]

Simplest asymptotic I can think of is the sides of a rectangle with a fixed area: xy=A. As you increase one of its sides the other side asymptotically approaches 0. The equation in your problem is similar: ε=BAω. If B and A are the variables, the relation between them will be asymptotic. If you increase B two times, you have to decrease A two times.

Linear relationship are abundant, for example potential energy U=mgh where m and g are constant. You can re-write this as U/h=mg=const. In this case if you increase h two times, you also have to increase U two times.