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:

$tan theta approx theta => tan3theta approx 3theta$

$sin theta approx theta => sin2theta approx 2theta$

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

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

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

$= 6$

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