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Thread: Need help with limits

  1. #1
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    Need help with limits

    Hiya,

    how would I calculate lim f(x)/g(x) =12/5 given that g(5)=0
    ..............................x->5

    I tried (x-5) must be a factor of g(x) then made up (5x+1)(x-5) expanded while keeping f(x) at 2x^2+a , then i tried splitting up 2x^2+a into the 5x^2-24x-5 so got (5x^2 -24x-5)-3x^2+24x+5+a but going around in circles...

    can someone confirm whether im doing this right please ? any steps ? thank you so muchhh
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  2. #2
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    Re: Need help with limits

    i kinda wanna know cuz im practising as i have exams soon so any advice appreciated ! so please can i have an explanation with methods steps shown so i understand how i can do it in the exam and my mates dont know and its the holidays so i cant ask the teacher and i kinda have a lot to get through

    stressful so much i need to study!

    hope you understand,
    thank you
    Last edited by DiscreteMathHelp; Apr 3rd 2017 at 12:15 PM.
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  3. #3
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    Re: Need help with limits

    what are $f(x)$ and $g(x)$ ?
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    Re: Need help with limits

    Quote Originally Posted by romsek View Post
    what are $f(x)$ and $g(x)$ ?
    Hiya, tysm for the response - I have to find f(x) and g(x), the purpose, sorry if i hadnt made myself clear.

    thanks!
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  5. #5
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    Re: Need help with limits

    $\displaystyle \lim_{x \to 5} \dfrac{x^2+2x-35}{x^2-5x} =$ ?
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    Re: Need help with limits

    Quote Originally Posted by DiscreteMathHelp View Post
    Hiya, tysm for the response - I have to find f(x) and g(x), the purpose, sorry if i hadnt made myself clear.

    thanks!
    well let's see

    $\displaystyle \lim_{x\to 5}~\dfrac{f(x)}{g(x)} = \dfrac {12}{5}$

    and $g(5)=0$

    yes, $g(x)$ must contain a factor of $x-5$

    so the slickest thing to do is set

    $f(x)=f_1(x)(x-5)$

    where $f_1(5) = \dfrac{12}{5}$

    $f_1(x) = \dfrac {12}{5} (6-x)$ will do this nicely so we end up with

    $f(x) = \dfrac{12}{5}(6-x)(x-5) = \dfrac 1 5 (-12 x^2+132 x-360)$

    $g(x) = (x-5)$

    or we might as well have

    $f(x) = -12 x^2+132 x-360$

    $g(x) = 5(x-5)$
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  7. #7
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    Re: Need help with limits

    Notice that romsek chose g(x) to be x- 5 and chose " f_1(x)" to be \frac{12}{5}(6- x). There are an infinite number of functions f(x) and g(x) that would work.
    Thanks from JeffM
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    Re: Need help with limits

    Quote Originally Posted by HallsofIvy View Post
    Notice that romsek chose g(x) to be x- 5 and chose " f_1(x)" to be \frac{12}{5}(6- x). There are an infinite number of functions f(x) and g(x) that would work.
    yeah but I didn't like any of the others, too tinny.
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    Re: Need help with limits

    Quote Originally Posted by romsek View Post
    yeah but I didn't like any of the others, too tinny.
    tysm
    honestly i really appreciated it, also i needed both that had degree 2 so i just timed both the equations by x, as i suppose as i should do...

    this seems like a really great forum, you guys saved me in an exam once before cuz something really similar came up !
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