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# Limit law question watch

1. I've been assigned a question that my class hasn't really done much work on

This is the question:

This is what I have done so far - I doubt it's correct though

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2. (Original post by TwiMaster)
I've been assigned a question that my class hasn't really done much work on

This is the question:

This is what I have done so far - I doubt it's correct though

Attachment 474449474451
Attachment 474449474451474400
the first can be done be a simple algebraic manipulation or L'Hospital Rule (limit is -1/9)
3. (Original post by TeeEm)
the first can be done be a simple algebraic manipulation or L'Hospital Rule (limit is -1/9)
My lecturer wants us to only use the limit laws to find the limit and then we actually have to prove it
4. (Original post by TwiMaster)
My lecturer wants us to only use the limit laws to find the limit and then we actually have to prove it
I am using rules/laws of limits but then again I do not know what you lecturer might be referring to.
I certainly not using epsilon-delta techniques in those 2 limits and I doubt (though not 100%) that this is what he is asking for here.
5. (Original post by TeeEm)
I am using rules/laws of limits but then again I do not know what you lecturer might be referring to.
I certainly not using epsilon-delta techniques in those 2 limits and I doubt (though not 100%) that this is what he is asking for here.
Oh okay, I think it would be fine anyway as long as the laws are used & it's proven to be correct
6. (Original post by TwiMaster)
Oh okay, I think it would be fine anyway as long as the laws are used & it's proven to be correct
the second one diverges, clearly seen if written as (3x+8)/(x+2) and think of it as the vertical asymptote of a curve

In the first one, rewrite it as

(1/x -1/3)/(x-3)

then either use L'Hospital Rule directly

or

simplify the numerator, remove the singularity, to end up with -1/(3x) which gives -1/9
7. (Original post by TeeEm)
the second one diverges, clearly seen if written as (3x+8)/(x+2) and think of it as the vertical asymptote of a curve

In the first one, rewrite it as

(1/x -1/3)/(x-3)

then either use L'Hospital Rule directly

or

simplify the numerator, remove the singularity, to end up with -1/(3x) which gives -1/9
yup I've managed to get lim -1/3x. Wouldn't this be the same as lim -1 / lim 3x
8. (Original post by TwiMaster)
yup I've managed to get lim -1/3x. Wouldn't this be the same as lim -1 / lim 3x
it is indeed
9. (Original post by TeeEm)
it is indeed
Thanks - the question also says that we need to state why we're allowed to use a specific limit law. Are there any special conditions?
10. (Original post by TwiMaster)
Thanks - the question also says that we need to state why we're allowed to use a specific limit law. Are there any special conditions?
I am an applied mathematician so not sure from a pure point of viw what exactly they mean, given I have not attended your lectures.

Do they mean rules such as Lim(f+g) = Lim(f )+ Lim(g)?

or do they mean epsilon techniques.

my advice is to wait for a purist just in case they can suggest something further.
11. (Original post by TeeEm)
I am an applied mathematician so not sure from a pure point of viw what exactly they mean, given I have not attended your lectures.

Do they mean rules such as Lim(f+g) = Lim(f )+ Lim(g)?

or do they mean epsilon techniques.

my advice is to wait for a purist just in case they can suggest something further.
yes, but in this case it would be lim (f/g) = lim (f)/ lim (g) that's being used but okay, hopefully a purist comes along
12. (Original post by TwiMaster)
yes, but in this case it would be lim (f/g) = lim (f)/ lim (g) that's being used but okay, hopefully a purist comes along
sure
that was an example (no addition of limits was used of course)
13. (Original post by TwiMaster)
This is what I have done so far - I doubt it's correct though
At the point where you had you should simply cancel down to get .

From here you should be able to simply finish using the laws you've been given about things like "the limit of a quotient = the quotient of the limits".

Similarly in the 2nd case you can simply rewrite the limit as

and again I would expect the limit laws you have would enable you to finish.

Perhaps the most important thing to realise here is that if you are asked to find , where f is some complicated function, then you can do whatever simplification you want to f without affecting the limit. This doesn't require any limit laws, since you're not actually changing f, just "writing it in a different way".

If you want more specific help you will need to post exactly what example 3.2, Theorem 3.6 etc. are.

I don't see how you can possibly use L'Hoptial etc. unless it is one of the named theorems you've been told you can use.
14. (Original post by DFranklin)
At the point where you had you should simply cancel down to get .

From here you should be able to simply finish using the laws you've been given about things like "the limit of a quotient = the quotient of the limits".

Similarly in the 2nd case you can simply rewrite the limit as

and again I would expect the limit laws you have would enable you to finish.

Perhaps the most important thing to realise here is that if you are asked to find , where f is some complicated function, then you can do whatever simplification you want to f without affecting the limit. This doesn't require any limit laws, since you're not actually changing f, just "writing it in a different way".

If you want more specific help you will need to post exactly what example 3.2, Theorem 3.6 etc. are.

I don't see how you can possibly use L'Hoptial etc. unless it is one of the named theorems you've been told you can use.
Ah thanks! I've simplified it to -1/3x and now this is what I'm left with:

15. (Original post by TwiMaster)
Ah thanks! I've simplified it to -1/3x and now this is what I'm left with:

I really think you need to post exactly what the theorems are that you're allowed to use. It's impossible to expect us to guess what you are / are not allowed to do.
16. (Original post by DFranklin)
I really think you need to post exactly what the theorems are that you're allowed to use. It's impossible to expect us to guess what you are / are not allowed to do.
Oh okay, never mind that question anyway. Are you familiar with squeeze theorem? I've also been asked to prove that sin3x/2x = 3/2 using this theorem but i'm not exactly sure how

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