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

1 Answer
May 13, 2018

= 6

Explanation:

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