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Math Help - Limit of a function

  1. #1
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    Limit of a function

    Some questions concerning limits.

    How do I sketch a graph when I'm given limit info, for example this
    lim f =2(as x approaches 0^-)
    lim f =0(as x approaches 4^+)
    lim f =0(as x approaches 0^+)
    lim f =3 ( as x approaches 4^-)
    f(0)=2
    f(4)=1

    I have some vague idea how to do it, but my sketches do not seem like graphs.

    Prove that lim sqrt(x)*e^(sin(pi:x)) =0(as x approaches 0^+)
    no idea where to start this, I could graph is on graphing calculator but that is worthless, i cannot use limit laws as e^sin(pi/x) doesnt exist as you cant divide by zero.

    Suppose that
    x^4<f(x)<x^2
    if |X|<1 and
    x^2<f(x)<x^4
    if |x|>1
    find value of limits
    lim f(x) as x approaches -1
    lim f(x) as x approaches 0
    lim f(x) as x approaches 1

    no clue about that one


    Last one I just wanna make sure I did right,
    is there a number c such that
    lim ((2x^2+cx-4c)/(x^2+x-6)) (as x approaches 2) exists?
    If so find value of c and calculate limit
    what i did is a bit of guessing
    factor x^2+x-6
    x^2+x-6=(x-2)(x+3)
    now this is where guessing comes in
    2x^2+cx-4c.
    D=c^2+32c
    so D must be a sqrt of something otherwise i cant see it being factored
    let c=4 then D=144 then
    2x^2+cx-4c=2x^2+4x-16=(x+4)(x-2)
    x-2 is canceled, therefore
    (x+4)/(x+3)
    rest is obvious.
    Forgive me for my wall of text and my poor understanding of math, any help is appreciated!
    Last edited by Wuffle; September 22nd 2011 at 04:29 PM.
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  2. #2
    MHF Contributor

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    Re: Limit of a function

    I wonder if anyone can read this post?
    It is totally unreadable as far as I can see.
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