Limits of Trig Functions

  • Thread starter erik05
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  • #1
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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.
 

Answers and Replies

  • #2
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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]
 
  • #3
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Sorry, I haven't learned l'hopitals rule yet and we're not suppose to use it for these questions.
 
  • #4
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expand tanx in taylor series, and do what you should do....
 
  • #5
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This is going to sound really pathetic but no, we haven't the taylor series either.
 
  • #6
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do you know the fact that
[tex] \lim_{x \rightarrow 0} \frac {sinx}{x} =1[/tex]
if yes, you should start from here
 
  • #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.
 
  • #8
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vincentchan said:
do you know the fact that
[tex] \lim_{x \rightarrow 0} \frac {sinx}{x} =1[/tex]
if yes, you should start from here

That I do know.
 
  • #9
dextercioby
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What about "tangent's" definition...?And the limit of cosine as its argument goes to 0 ?

Daniel.
 
  • #10
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erik05 said:
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.

= 1/4*(sin[x]/x)*(sec[x])
 
  • #11
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Ah...I got it. Thanks all.
 
  • #12
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Limit Laminate...


Solution:
[tex] \boxed{\lim_{x \rightarrow 0} \frac {\tan x}{4x} = \frac{1}{4}}[/tex]
 
Last edited:
  • #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:

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