I think this is one of the things that calculus screws my train of thought on.

 

I think I understand what a limit is. Why would you have to define a limit? Is there ever a situation where not defining a limit would change the outcome?

What exactly do you mean? Are you asking why one would define a limit instead of just trying to solve the problem without a limit?

pretty much yeah If a function is going to go towards something regardless.....

How about a function like

 

[math]f(x) = \frac{x^2 - 4}{x+2}[/math]

 

Find f(-2).

 

The function doesn't exist at all at x = -2, but with a limit you can find what that function would be at x = -2.

Most of the time, you don't need to worry about limits. But both derivatives and integrals are based on limits, and to use them you need a formal, mathematically precise definition for limits or you might as well not be doing math.

But both derivatives and integrals are based on limits

 

This is it right here. This is the whole point of learning limits, because the basic definitions in calculus depend on that definition. If it isn't clear now, it should become clear in the near future.