Question

How does (sin2x)/x=2?

Answer 1

This came from the question of finding the limit of (tan2x)/x as x approaches 0

Answer 2

\[\sin ( 2x ) = 2 \sin (x) \cos (x)\]

Answer 3

\[\lim_{x \rightarrow 0} \frac{ \sin x } {x} = 1\]

Answer 4

important trig identity to remember

also you should memorize that limit as well

Answer 5

I still don't see how sin(2x)/x=2

Answer 6

substitute sin (2x) for 2 sin x cos x

Answer 7

ok but as x approaches 0, the answer becomes 0

Answer 8

look at the limit i wrote above
its a special case

Answer 9

I understood that part, you get that from the sqeeze theorem. So your saying that because we multiplied x by 2, we automatically get 2?

Answer 10

and as the denominator approahces zero, the limit is infinity not zero

Answer 11

no im saying, you factor out sinx /x

since that is equal to 1

you are left with finding the limit of 2 cos x as x approaches 0

Answer 12

oh... thanks I got it now

Answer 13

no prob

Answer 14

\[\lim_{x \rightarrow 0\frac{ \sin2x }{ x }}=2\lim_{x \rightarrow 0}\frac{ \sin 2x }{ 2x }=2*1=2\]
\[\lim_{x \rightarrow 0} \rightarrow \lim_{2x \rightarrow0 }\]