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    (Original post by Mr M)
    Well I suppose it is an appropriate time of year to teach your grandmother to suck eggs.
    (Original post by Mr M)
    Eh?
    Hhmm
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    (Original post by Jackabc)
    Hhmm
    Not an insult.

    http://en.wikipedia.org/wiki/Teachin...r_to_suck_eggs
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    Sorry I am an idiot, tired and sensitive. I thought you was telling me to suck her balls lol
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    Btw do you know how find the horizontal asymptote of a rational function, well do you know how to sketch them in general? There is not much advice in the textbook.

    For something like 7x/(3x+1)
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    (Original post by Jackabc)
    Btw do you know how find the horizontal asymptote of a rational function, well do you know how to sketch them in general? There is not much advice in the textbook.

    For something like 7x/(3x+1)
    Yes.

    Write it in divided out form.

    \displaystyle \frac{7x}{3x+1} = A + \frac{B}{3x+1}

    Then the horizontal asymptote is y = A.
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    (Original post by Jackabc)
    Btw do you know how find the horizontal asymptote of a rational function, well do you know how to sketch them in general? There is not much advice in the textbook.

    For something like 7x/(3x+1)
    Polynomial division? You've basically got 7/3 + some fraction which will tend to 0 as x gets bigger.
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    (Original post by Mr M)
    Yes.

    Write it in divided out form.

    \displaystyle \frac{7x}{3x+1} = A + \frac{B}{3x+1}

    Then the horizontal asymptote is y = A.
    (Original post by davros)
    Polynomial division? You've basically got 7/3 + some fraction which will tend to 0 as x gets bigger.
    Why exactly does that work?
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    (Original post by Jackabc)
    Why exactly does that work?
    Davros explained it really. The fraction approaches zero for large and small x so can (almost) be ignored.

    Edit: Small here means large negative.
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    (Original post by Jackabc)
    Why exactly does that work?
    Not sure what you're asking? If the numerator and the denominator are both linear (Ax + B) then you can always divide the bottom into the top and get an expression in the form MrM wrote.

    As x gets bigger then the remainder with the linear factor in the denominator gets smaller and smaller, so y gets closer and closer to the constant term which is therefore the horizontal asymptote.
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    (Original post by Mr M)
    Yes.

    Write it in divided out form.

    \displaystyle \frac{7x}{3x+1} = A + \frac{B}{3x+1}

    Then the horizontal asymptote is y = A.
    (Original post by davros)
    Polynomial division? You've basically got 7/3 + some fraction which will tend to 0 as x gets bigger.
    Why exactly does that work?

    (Original post by Mr M)
    Yes.

    Write it in divided out form.

    \displaystyle \frac{7x}{3x+1} = A + \frac{B}{3x+1}

    Then the horizontal asymptote is y = A.
    (Original post by davros)
    Polynomial division? You've basically got 7/3 + some fraction which will tend to 0 as x gets bigger.
    I think I get why actually now. Would this work if the polynomial on top had degree 2 and the denominator degree 3?

    Edit: Just saw what you said but does that only work for certain cases? Doesn't matter if it takes too long to explain as probably don't need to know too much just interesting.
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    (Original post by Jackabc)
    I think I get why actually now. Would this work if the polynomial on top had degree 2 and the denominator degree 3?
    Other way up. If the numerator has degree 3 and the denominator 2 then you get an oblique (wonky) asymptote of the form y = Ax + B.
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    (Original post by Mr M)
    Other way up. If the numerator has degree 3 and the denominator 2 then you get an oblique (wonky) asymptote of the form y = Ax + B.
    How an earth do you know all this? You must have a good textbook because mine hardly explains anything, either that or I am just stupid.
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    Use quotient rule
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    (Original post by Jackabc)
    How an earth do you know all this?
    I'm a mathematics teacher.
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    (Original post by Mr M)
    I'm a mathematics teacher.
    Oh right, do you enjoy it as I was hoping one day to be a teacher but if the work outside of school was too much then might not be worth it. Do you think textbooks are crap these days as they hardly explain any knowledge?
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    (Original post by Jackabc)
    Oh right, do you enjoy it as I was hoping one day to be a teacher but if the work outside of school was too much then might not be worth it. Do you think textbooks are crap these days as they hardly explain any knowledge?
    It's ok. I do lots of work outside school but I could do less if I wanted. I think most textbooks are perfectly fine but it is a good idea to refer to a range of sources on obscure topics.
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    (Original post by Mr M)
    It's ok. I do lots of work outside school but I could do less if I wanted. I think most textbooks are perfectly fine but it is a good idea to refer to a range of sources on obscure topics.
    I suppose, its just sometimes I wonder why is that the case and I think the textbooks bad but it could be out of syllabus. For example in s2 when finding E(x) for a p.d.f it just says replace the sum sign by an integral sign but I don't get how it gives the sum of the probabilities multiplied by x as f(x) is not a probability if you get what I am saying. Is that something I will find out at uni or am I missing something? Last question I promise
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    (Original post by Jackabc)
    I suppose, its just sometimes I wonder why is that the case and I think the textbooks bad but it could be out of syllabus. For example in s2 when finding E(x) for a p.d.f it just says replace the sum sign by an integral sign but I don't get how it gives the sum of the probabilities multiplied by x as f(x) is not a probability if you get what I am saying. Is that something I will find out at uni or am I missing something? Last question I promise
    you would really need to study the fundamentals at uni - it's a principle that crops up in different areas. Basically, the integral is the limiting form of a sum so when you move from a discrete distribution to a continuous one the simple formula you have that involves a sum becomes a more complicated formula involving an integral and a probability density.
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    (Original post by davros)
    you would really need to study the fundamentals at uni - it's a principle that crops up in different areas. Basically, the integral is the limiting form of a sum so when you move from a discrete distribution to a continuous one the simple formula you have that involves a sum becomes a more complicated formula involving an integral and a probability density.
    Thanks a lot for all your help. This is why I don't like a-level maths, its almost empty of meaning but like you said, at uni it isn't. Is it safe to assume that anything that the textbook doesn't explain is not meant to be explained?
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    (Original post by Jackabc)
    Thanks a lot for all your help. This is why I don't like a-level maths, its almost empty of meaning but like you said, at uni it isn't. Is it safe to assume that anything that the textbook doesn't explain is not meant to be explained?
    Sorry I didn't see your question. Some explanations are avoided as they are simply too difficult and some explanations are omitted because they are beyond the scope of the course and there isn't sufficient space to cover everything in the depth the authors might like. There is nothing to stop you from reading further though ...

    Edit: It only took a couple of minutes to find a link.
 
 
 
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