## anonymous 5 years ago What would be the simplest definition for an asymtote?

1. amistre64

something to snuggle up to

2. amistre64

an asymptote tends to be a boundary line that is forever approached; getting closer and closer; but never reaching unless you can get all the way to the end of infinity

3. anonymous

actually that is not quite right

4. amistre64

and horizontals and slants can be croseed; but in the end they act right

5. anonymous

A line at a limit

6. amistre64

now now; he said simple definition; not accurate definintion lol

7. anonymous

for example $\frac{\sin(x)}{x}$ certainly approaches 0 as x increases, but it crosses infinitely many times

8. anonymous

You need to properly define what a limit is to rigorously describe what it is.

9. anonymous

i think the question should be "what is the definition" of an asymptote" rather than "simplest"

10. anonymous
11. anonymous

Also I guess it should be noted that other functions can be asymptotes (for instance you can have polynomial asymptotes with degree greater than 1)

12. anonymous

I quite like "tangent at infinity" even if u can pick holes in it...

13. anonymous

A straight line that defines limits of a curve.