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

Cleavage

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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.
 

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anytime before 10am tomorrow, I'll be cheering
 

VBN2470

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should do.

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

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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

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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

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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

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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

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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

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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

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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.
 

InteGrand

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

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