Find the following limit as x->0

  • #1
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find the following limit as x-->0

Hello I am trying to find the following limit as x-->0. I have tried using l'hopital's rule but all it produces is a more complex thing i still can't take the limit of. any help?
[tex]\frac{sin x - x}{sin^3(x)}[/tex]
I can see this limit exists on the graph i just dont know how to go about solving it.
 

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  • #2
arildno
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Take L'hopital once.
Then multiply your expression with [tex]1=\frac{\cos(x)+1}{\cos(x)+1}[/tex]
 
  • #3
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Thanks this worked. One question about this is how did you know to multiply by this? How would one know to do this when faced with similar situations
 
  • #4
Hurkyl
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You could have just done L'Hôpital again.

arildno just factored the denominator (after converting sin² to cos²).
 
  • #5
arildno
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thenewbosco said:
Thanks this worked. One question about this is how did you know to multiply by this? How would one know to do this when faced with similar situations
Just practice&patience.
To think of simple tricks like this comes naturally to you if you have worked assiduously with your maths earlier.
 
  • #6
arildno
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Hurkyl said:
You could have just done L'Hôpital again.

arildno just factored the denominator (after converting sin² to cos²).
Factorization is more fun.
 

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