Find the limit. lim _(xarrow 0)(tan(12x))/(sin(11x))= square

To find the limit of the given expression, we can use the fact that . Then, we can apply the limit to the numerator and denominator separately. Now, we can apply the limit to the numerator and denominator separately: As approaches 0, and both approach 0, while approaches 1. Therefore, the limit of the expression is: This is an indeterminate form, so we need to use L'Hopital's rule. L'Hopital's rule states that if the limit of the numerator and denominator both approach 0 or both approach infinity, we can take the derivative of the numerator and denominator separately and then find the limit.Taking the derivative of the numerator and denominator with respect to , we get: Now, we can apply L'Hopital's rule: As approaches 0, and both approach 1, while approaches 0. Therefore, the limit of the expression is: Therefore, the limit of the given expression is .