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Finding limits

  1. Jul 11, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the limit:

    lim (tanx-1)/(x-pi/4)
    x->pi/4


    2. Relevant equations
    tanx = sinx/cosx


    3. The attempt at a solution

    lim (sinx/cosx-1)/(x-pi/4)
    x->pi/4

    lim [(sinx-cosx)/cosx]/(x-pi/4)
    x->pi/4

    I have no idea what to do after this ): I also tried squaring the whole function and getting tan2x-1 = sec2x, but I get so lost on what to do with pi/4 because it just keeps becoming undefined!

    Thanks for your help!!
     
  2. jcsd
  3. Jul 11, 2011 #2

    micromass

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    Hi Glissando! :smile:

    I take it you're not allowed to use L'hopitals rule?? In that case, I would first write

    [tex]\tan(x)=\tan((x-\pi/4)+\pi/4)[/tex]

    and work that out. That way you can write everything in function of [itex]x-\pi/4[/itex].
     
  4. Jul 11, 2011 #3
    Hi micromass,

    Thanks for your quick response! I'm not too sure what you mean by working it out...do I plug that back into the original equation? Am I solving for x?

    Thanks!
     
  5. Jul 12, 2011 #4

    micromass

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    Well, you know formula's for [itex]\tan(\alpha+\beta)[/itex]. So apply these formula's on

    [tex]\tan((x-\pi/4)+\pi/4)[/tex]

    Our goal is to write everything in function of [itex]x-\pi/4[/itex]
     
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