Find the limit as x approaches 0, (sin^2 x)/x

I'm a bit confused as to what to do because the sin is squared. I can convert that into (sinx^2)/x I believe, but I'm still not sure what to do then?

Question

Find the limit as x approaches 0, (sin^2 x)/x

I'm a bit confused as to what to do because the sin is squared. I can convert that into (sinx^2)/x I believe, but I'm still not sure what to do then?

tkhunny · Answer

Super big hint: $\dfrac{\sin^{2}(x)}{x} = x\cdot\dfrac{\sin^{2}(x)}{x^2} = x\cdot\left(\dfrac{\sin(x)}{x}\right)^{2}$

anonymous · Answer

wouldn't that end up being 1^2 which is just 1? Cause sin(x)/x equals 1. and x * 1 would still equal one, so it'd be 1^2? My answer key says it is 0 though?

tkhunny · Answer

What did you do with that extra 'x' out in front?

anonymous · Answer

wouldn't i multiply that x by 1? cause you have it as x * (sinx/x) which is basically x * 1 correct?

tkhunny · Answer

And x is approaching 0?

anonymous · Answer

oh hah, I forgot to substitute that in! dumb mistake on my part. thanks.