Why are limits important?

Question

anonymous · Answer

just like in general all help is appreciated :D

anonymous · Answer

Well that's a pretty vague question, but I'll tell you some uses I've had for limits.

Limits help predict behavior at a point where behavior cannot be predicted. So, for example, we can take the limit of a function as it approaches a value the function does not exist at to get an idea of how it behaves around that point.

Limits are also good for determining future behavior. So, for example, in my Mathematical Biology class, we would examine diseases modeled by equations like:
$$ f(t) = \frac{2100}{700 + e^{-2.1t}} $$
And our teacher would ask, "How will this disease behave in the long run?" Thus we take the limit of the above equation as t goes to infinity. Sometimes the limit would show the disease will become out of control, thus people need to be vaccinated now to help control. Sometimes diseases will stabilize. It all depends on what the limit gives.

Hopefully that helps! GREAT question by the way! It's always important to ask "why" in mathematics.

tyteen4a03 · Answer

I was going to draw up some kind of conclusion but @chipperdrew was way better than me :P

anonymous · Answer

haha yes it is a very vague question sorry but i have this project and i came to the realization that, wow I've been studying derivatives (soon integrals) and i just forgot what limits were! i was just looking for a big summary and you helped a lot!!! thanks :D

anonymous · Answer

Don't worry @tyteen4a03 you still win the avatar battle ;)

tyteen4a03 · Answer

@chipperdrew I was going to include this joke: If we didn't have limits we would be able to steal games from the store and murder teachers we don't like.

Oh well :P