Final answer:
The limit of tan(6t)sin(3t) as t approaches 0 is 0.
Step-by-step explanation:
To find the limit lim(t → 0) tan(6t)sin(3t), we can use the fact that the limit of a product is equal to the product of the limits, provided the limits exist. First, we can simplify the expression by recognizing that tan(6t)/sin(6t) = 6. So, the limit becomes lim(t → 0) 6sin(3t). Now, we can use the fact that the limit of a constant times a function is equal to the constant times the limit of the function. The limit of sin(3t) as t approaches 0 is 0. Therefore, the final limit is 6 * 0 = 0.