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anonymous

  • 4 years ago

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?

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  1. anonymous
    • 4 years ago
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    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.

  2. anonymous
    • 4 years ago
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    Try substituting C*x for x and compute with L'Hopitals rule. You will see that by the chain rule, the constant drops out.

  3. anonymous
    • 4 years ago
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    = limit dsinx dx = cos x -------- dx/dx lmt >0 of cos x = 1

  4. anonymous
    • 4 years ago
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    \[ \lim_{x\rightarrow 0} \frac{\sin(C x)}{Cx} = \lim_{x\rightarrow 0} \frac{C\cos(Cx)}{C} = \frac{C}{C}\cdot \cos(C\cdot 0) = \cos(0) = 1 \]

  5. Zarkon
    • 4 years ago
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    \[\frac{\pi}{180}\]

  6. anonymous
    • 4 years ago
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    Thanks again guys.

  7. Zarkon
    • 4 years ago
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    Just to make sure...the answer is not 1. it is \[\frac{\pi}{180}\]

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