Lim as x goes to 0:
(2sinxcosx)/2x

i'm pretty sure i have it right (answer being 1) but i'd like an explanation to compare to my own.

They want you to make use of this limit identity:



y=sin(x) and y=x approach zero at the same rate.

So with your problem you simply apply your Sine Double Angle Identity,



From this point, hopefully you can see that we have our identity with t=2x. So yes, you are correct :) the result is 1.