## 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?

1. 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.

2. 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.

3. anonymous

= limit dsinx dx = cos x -------- dx/dx lmt >0 of cos x = 1

4. anonymous

$\lim_{x\rightarrow 0} \frac{\sin(C x)}{Cx} = \lim_{x\rightarrow 0} \frac{C\cos(Cx)}{C} = \frac{C}{C}\cdot \cos(C\cdot 0) = \cos(0) = 1$

5. Zarkon

$\frac{\pi}{180}$

6. anonymous

Thanks again guys.

7. Zarkon

Just to make sure...the answer is not 1. it is $\frac{\pi}{180}$