The limit of the function tan 6x/sin 2x as x approaches zero is determined by first substituting x by zero. This is equal to zero over zero which is indeterminate. Using L'hopital's rule, we derive each term in the numerator and denominator separately. This is equal to 6 sec^2 x / 2 cos 2x. when substituted with zero again, the limit is 1/2.
