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Homework Help: General Limits Problem

  1. Aug 31, 2009 #1
    1. The problem statement, all variables and given/known data
    All the problem is asking me to do is find the limit. I have to do it algebraicly too which sucks. I can't figure out how to do it.
    [tex]\lim_{x\rightarrow0} \frac{\frac{1}{x+2}-\frac{1}{2}}{x}[/tex]

    2. Relevant equations

    I am not sure really.

    3. The attempt at a solution
    One thing I have tried is to multiply by [tex]\frac {x}{x}[/tex]. Which gave me:
    [tex]\lim_{x\rightarrow0} \frac{\frac{1}{x+2}-\frac{1}{2}}{x} \times \frac {x}{x}[/tex]

    [tex]=\frac{\frac{1\times x}{x+2}-\frac{1\times x}{2}}{x\times x}[/tex]

    [tex]= \frac{\frac{x}{x+2}-\frac{x}{2}}{x^{2}}[/tex]

    [tex]=\frac{x}{x+2}\rightarrow \frac{x}{x}+\frac{x}{2} \rightarrow 1+\frac{x}{2}[/tex]



    1) I am not sure of my algebra during this and
    2) I don't know where to go from here should my algebra check out.

    I have already tried to multiply by [tex]\frac{\sqrt{x}}{\sqrt{x}}[/tex] but it just seems to give me [tex]\frac{\sqrt{x}}{x}[/tex] which doesn't help. I am stuck help me please?
  2. jcsd
  3. Aug 31, 2009 #2


    Staff: Mentor

    Combine the two fractions in the numerator and then simplify the whole thing.
  4. Aug 31, 2009 #3
    Thank you!!!!!!! :):):):):):):):)
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