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Limits of Trig Functions

  1. Apr 19, 2005 #1
    Hello all. I missed a class in calculus so I didn't get the notes on this so if anyone could explain this question for me, it would be much appreciated.

    [tex] \lim_{x \rightarrow 0} \frac {tanx}{4x} [/tex]
    [tex]= \frac {sinx}{cos4x} ? [/tex]

    Not really too sure if I manipulated the equation right. Any hints for the next step? Thanks.
     
  2. jcsd
  3. Apr 19, 2005 #2
    You can't do that!!!!!



    Use l'hopitals rule.

    [tex] \lim_{x \rightarrow 0} \frac {tanx}{4x} =\lim_{x \rightarrow 0} \frac {secxtanx}{4}[/tex]
     
  4. Apr 19, 2005 #3
    Sorry, I haven't learned l'hopitals rule yet and we're not suppose to use it for these questions.
     
  5. Apr 19, 2005 #4
    expand tanx in taylor series, and do what you should do....
     
  6. Apr 19, 2005 #5
    This is going to sound really pathetic but no, we haven't the taylor series either.
     
  7. Apr 19, 2005 #6
    do you know the fact that
    [tex] \lim_{x \rightarrow 0} \frac {sinx}{x} =1[/tex]
    if yes, you should start from here
     
  8. Apr 19, 2005 #7

    dextercioby

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    I think Taylor series is taught way after l'Hôpital's rule,don't u think so?:rolleyes:

    Daniel.
     
  9. Apr 19, 2005 #8
    That I do know.
     
  10. Apr 20, 2005 #9

    dextercioby

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    What about "tangent's" definition...?And the limit of cosine as its argument goes to 0 ?

    Daniel.
     
  11. Apr 20, 2005 #10
    = 1/4*(sin[x]/x)*(sec[x])
     
  12. Apr 20, 2005 #11
    Ah...I got it. Thanks all.
     
  13. Apr 20, 2005 #12
    Limit Laminate...


    Solution:
    [tex] \boxed{\lim_{x \rightarrow 0} \frac {\tan x}{4x} = \frac{1}{4}}[/tex]
     
    Last edited: Apr 20, 2005
  14. Apr 20, 2005 #13

    dextercioby

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    How fancy that \boxed{...},too bad u don't know "\tan"...:rolleyes:

    Daniel.

    P.S.BTW,I've searched Mathworld and A & S,couln't find this [itex] tanx [/itex] function... :bugeye:

    P.P.S.Neither [itex] sinx[/itex],nor [itex] secxtanx [/itex],but i found [itex] \mbox{sinc}\ x [/itex]... :surprised

    P.P.P.S.You edited... :wink:
     
    Last edited: Apr 20, 2005
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