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Math Help - Limits - find parameters α , β

  1. #1
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    Limits - find parameters α , β

    I am given this limit and am asked to find parameters α and β

    \lim _{x \mapsto 1 } \frac{x^2 + \alpha x + \beta}{x^2 - 1} = 2
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  2. #2
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    Re: Limits - find parameters α , β

    Quote Originally Posted by theintervurt View Post
    I am given this limit and am asked to find parameters α and β

    \lim _{x \mapsto 1 } \frac{x^2 + \alpha x + \beta}{x^2 - 1} = 2

    You want x^2 + \alpha x + \beta=(x-1)(x+c) so
    c-1=\alpha\\-c=\beta\\1+c=4.
    Thanks from theintervurt
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    Re: Limits - find parameters α , β

    Thanks, I do understand the reasoning behind this however I am curious is there another way of going about it without having to introduce a new parameter (c) ?

    Also here is another similar case which I can't solve

    \lim _{x\mapsto 0} \frac {\gamma + \delta \sin {x}}{x^2} = 3

    again I have to find γ and δ however I haven't been able to figure out how to proceed
    Last edited by theintervurt; February 5th 2013 at 12:12 AM.
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    Re: Limits - find parameters α , β

    Quote Originally Posted by theintervurt View Post
    Thanks, I do understand the reasoning behind this however I am curious is there another way of going about it without having to introduce a new parameter (c) ?
    Also here is another similar case which I can't solve
    \lim _{x\mapsto 0} \frac {\gamma + \delta \sin {x}}{x^2} = 3

    First, Never, never continue an existing thread with a new question.
    With a new question always start a new thread.

    Now, as written \lim _{x\mapsto 0} \frac {\gamma + \delta \sin {x}}{x^2} = 3 has no solution.

    If it were \lim _{x\mapsto 0} \frac {\gamma x + \delta \sin {x}}{x^2} = 3 there is a solution.

    Now, I am absolutely not a fan of using l'Hopital's rule for limits, but in this case it is useful.
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