Easy as limits question so you should help all the first year unsw actl kids (1 Viewer)

[Cleavage]

Using the delta-epsilon definition of a limit, prove the value of the limit y = (x+3)/(x^2-3) as x approaches infinity. (find the limit + prove it).

One line of working in the definition has stumped me, I'm sure the person answering this question will be able to work it out.

 

[Cleavage]

anytime before 10am tomorrow, I'll be cheering

 

[mreditor16]

What a coincidence - I'm stuck on this Q as well. anyone?

 

[VBN2470]

should do.

Realise that , so use this to find a value of so that whenever you will have that .

 

[mreditor16]

What do you guys think about this proof?

 

[Amundies]

haha delta-epsilon definitions of limits were the thing that I struggled with the worst. Didn't understand it back then, still don't.

 

[InteGrand]

Alternatively, you can change the denominator into , since for x> 3, if , then also (note the limit is 0).

Edit: mreditor16 just posted this. Yes, that's valid.

 

[mreditor16]

Alternatively, you can change the denominator into , since for x> 3, if , then also (note the limit is 0).

Edit: mreditor16 just posted this. Yes, that's valid.

Is my whole proof correct? I am iffy about the last part.

 

[InteGrand]

Wait, why is M just 3.

 

[InteGrand]

Is my whole proof correct? I am iffy about the last part.

Just use (assuming the rest of the algebra etc. is right, I just skimmed over it; I meant the idea of using on denominator is valid).

 

[mreditor16]

Just use (assuming the rest of the algebra etc. is right, I just skimmed over it; I meant the idea of using on denominator is valid).

but you know how when you make such an assumption. at the end, you need to say m = min ( or )

like yeah. can someone please properly go through my proof?

 

[InteGrand]

but you know how when you make such an assumption. at the end, you need to say m = min ( or )

like yeah. can someone please properly go through my proof?

When did anyone say to use min?

 

[mreditor16]

When did anyone say to use min?

That's something we've learnt along the way, with these proofs, when you make such an assumption :/

 

[InteGrand]

And in general, should depend on (unless for example its a trivial limit, like proving the limit of a constant function etc.). I like to write to stress that it's a function of .

 

[InteGrand]

That's something we've learnt along the way, with these proofs, when you make such an assumption :/

Really? Often min is used for proving limit theorems, like sum rule for limits etc. But for these simple epsilon delta proofs for a function, it's usually not the case.

 

[mreditor16]

so is M = 3 or M = 3 + 1/epsilon ? :O

 

[InteGrand]

Yes

 

[InteGrand]

And more precisely, it can be (that's not the only possible M).

 

[mreditor16]

Yes

Yes to what lol?

 

[InteGrand]

Yes to what lol?

Yes to "so is M = 3 or M = 3 + 1/epsilon ? :O"