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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?
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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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0This 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
 4 years ago
Best ResponseYou've already chosen the best response.0Try substituting C*x for x and compute with L'Hopitals rule. You will see that by the chain rule, the constant drops out.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0= limit dsinx dx = cos x  dx/dx lmt >0 of cos x = 1

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[ \lim_{x\rightarrow 0} \frac{\sin(C x)}{Cx} = \lim_{x\rightarrow 0} \frac{C\cos(Cx)}{C} = \frac{C}{C}\cdot \cos(C\cdot 0) = \cos(0) = 1 \]

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.0Just to make sure...the answer is not 1. it is \[\frac{\pi}{180}\]
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