How do you evaluate #lim_(theta->0)# #((sin2thetatan3theta)/theta^2)#?

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Answer 1 · 2018-05-13T09:37:44

# = 6 #

Use small angle approximations:

# tan theta approx theta => tan3theta approx 3theta #

#sin theta approx theta => sin2theta approx 2theta #

#=> lim_(theta to 0 ) (2theta * 3theta) / theta^2 #

#=> lim_(theta to 0 ) ( (6theta^2) / theta^2 ) #

#=> lim_(theta to 0 ) ( 6 ) #

# = 6 #