anonymous
  • anonymous
lim -> 0 sin(2x) /(x*cos(x) ) help
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
sin (2x) = 2sin(x)cos(x) so sin(2x) /(x*cos(x) =2sin(x)cos(x)/x*cos(x)=2sinx/x which as x->0 goes to 1
anonymous
  • anonymous
no, answer is 2
anonymous
  • anonymous
ups sry, forgot about 2 multuplying: lim 2sinx/x=2*1=2 x->0

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anonymous
  • anonymous
don't undestand you
anonymous
  • anonymous
sin (2x) can be written like: sin (2x) = 2sin(x)cos(x) substituting this expretion in the original one: sin(2x) /(x*cos(x) =2sin(x)cos(x)/x*cos(x)=2sinx/x taking limits, and noticing that lim as x->0 of sinx/x=1: lim 2sinx/x=2*1=2 x->0
anonymous
  • anonymous
|dw:1352667129469:dw|
anonymous
  • anonymous
no
anonymous
  • anonymous
why not? l'Hôpital rule
anonymous
  • anonymous
yes, using l'hospital's rule works
anonymous
  • anonymous
Don't break your head ! You know that sin(x)=x as x tends to zero. So sin(2x) = 2x. In the denominator, keep x as it is and cos(x)=1. Hence the answer
anonymous
  • anonymous
thanks, but the image is ok?
anonymous
  • anonymous
|dw:1352669528245:dw|
lopus
  • lopus
claro que es posible es solamente derivar arriba y abajo como lo muestras en la imagen y ya

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