Question

What is the limit as x goes to zero for: ((sin(3x))/((sin(6x))?

Answer 1

3/6=1/2

Answer 2

ok, that was straight fwd; I got it right!

Answer 3

I think :-)

Answer 4

\[\lim_{x \rightarrow 0}\frac{\sin(3x)}{3x}*\frac{6x}{\sin(6x)}*\frac{3}{6}\]

Answer 5

thanks, that makes sense!

Answer 6

1*1*3/6

Answer 7

:)

Answer 8

Or you could do:
\[\lim_{x \rightarrow 0}\frac{\sin(3x)}{2\sin(3x)\cos(3x)}=\lim_{x \rightarrow 0}\frac{1}{2\cos(3x)}=\frac{1}{2\cos(0)}=\frac{1}{2}\].

Answer 9

Using the double angle formula: sin(2x)=2sin(x)cos(x)