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

    This is the question:

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

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

    This is the question:

    Name:  Photo 01-11-2015, 18 14 28.jpg
Views: 84
Size:  57.9 KB

    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)
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    (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
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    (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.
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    (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
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    (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
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    (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
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    (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
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    (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?
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    (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.
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    (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
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    (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)
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    (Original post by TwiMaster)
    This is what I have done so far - I doubt it's correct though
    At the point where you had \lim_{x \to 3}\dfrac{3-x}{3x(x-3)} you should simply cancel down to get \lim_{x \to 3} \dfrac{-1}{3x}.

    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

    \lim_{x \to -2} \dfrac{3x+8}{x+2} 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 \lim_{x \to a} f(x), 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.
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    (Original post by DFranklin)
    At the point where you had \lim_{x \to 3}\dfrac{3-x}{3x(x-3)} you should simply cancel down to get \lim_{x \to 3} \dfrac{-1}{3x}.

    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

    \lim_{x \to -2} \dfrac{3x+8}{x+2} 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 \lim_{x \to a} f(x), 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:

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

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    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.
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    (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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