SOLUTION: as t approaches 0 find the limit of ( (sin^2) (3t) ) / (t^2)

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Question 347870: as t approaches 0
find the limit of
( (sin^2) (3t) ) / (t^2)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use L'Hopital's rule.
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f(x)=%28sin%283t%29%29%5E2
f1(x)=f'(x)=6sin%283x%29cos%283x%29
f2(x)=f''(x)=18cos%5E2%283x%29-18sin%5E2%283x%29
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g(x)=x%5E2
g1(x)=g'(x)=2x
g2(x)=g''(x)=2
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f2%28x%29%2Fg2%28x%29=9cos%5E2%283x%29-9sin%5E2%283x%29
lim+%28x-%3E0%2C+f2%28x%29%2Fg2%28x%29%29=9%281%29-9%280%29=highlight%289%29