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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. Thanks!

1 Answer

1 vote
They want you to make use of this limit identity:


\rm \lim\limits_(t\to0)(sin(t))/(t)=1

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

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


\rm \lim\limits_(x\to0)(2sin x cos x)/(2x)=\lim\limits_(x\to0)(sin(2x))/(2x)

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