anonymous
  • anonymous
limx→0 sin x/x I understand that this is 1 when we are talking about radians... but the question says x is measured in degrees... What do?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
This doesn't make any difference, because you change a quantity x given in degrees into radians by multiplying with a constant C, where \[ C = \frac{360^\circ}{2\pi} \] Notice that when x goes to zero, C*x still goes to zero. So this is nothing but scaling your quantity.
anonymous
  • anonymous
Try substituting C*x for x and compute with L'Hopitals rule. You will see that by the chain rule, the constant drops out.
anonymous
  • anonymous
= limit dsinx dx = cos x -------- dx/dx lmt >0 of cos x = 1

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anonymous
  • anonymous
\[ \lim_{x\rightarrow 0} \frac{\sin(C x)}{Cx} = \lim_{x\rightarrow 0} \frac{C\cos(Cx)}{C} = \frac{C}{C}\cdot \cos(C\cdot 0) = \cos(0) = 1 \]
Zarkon
  • Zarkon
\[\frac{\pi}{180}\]
anonymous
  • anonymous
Thanks again guys.
Zarkon
  • Zarkon
Just to make sure...the answer is not 1. it is \[\frac{\pi}{180}\]

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