Here we see a dialogue where students discuss combining limits with arithmetic.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley, I’ve been thinking about limits.
Riley
So awesome!
Devyn
Think about This is the number that gets nearer and nearer to, as gets nearer and nearer to .
Riley
You know it!
Devyn
So I think it is the same as
Riley
Yeah, that does make sense, since when you add two numbers, say you get
Riley
Right! And I think the same reasoning will work for multiplication! So we should be able to say
Devyn
Yes, I think that’s right! But what about division? Can we use similar reasoning to conclude
Give an argument (similar to the one above) supporting the idea that

For the next problems, suppose is a number near and that is a number near .

Using the context above,
‘‘large’’ ‘‘small’’ impossible to say
Using the context above,
‘‘large’’ ‘‘small’’ impossible to say