Calculus Trig Function Limits

[biochemtx]

<p>Can someone help me find the limit of sin(sin(2x)/x as x approaches 0? Im looking at my hw notes and all these trig function limits are easy but this one is confusing me.</p>

<p>If i multiply top and bottom by 2x i can cancel out the sin2x but what is left in the parentheses of the first sin? sin(??) *2. I know the answer is 2, but what is the justification</p>

[Desafinado]

<p>multiply the top and bottom by 2. This will give you 2sin(2x)/2x. Multiply out the 2/1 so you have 2/1 * sin(2x)/2x. Because sin(x)/x=1, sin(2x)/2x=1. Then that 1 is multiplied by the other 2/1.</p>