Final answer:
The limit of sin(3x)/x as x approaches infinity is 0.
Step-by-step explanation:
The given limit is limx →∞ sin(3x)/x. To find the limit, we can use L'Hôpital's Rule. Differentiating both the numerator and the denominator, we get (3cos(3x))/1. Since the limit as x approaches infinity is a certain type of indeterminate form (0/0), we need to apply L'Hôpital's Rule again. Differentiating once more, we get -9sin(3x)/1. Now, as x approaches infinity, sin(3x) oscillates between -1 and 1, so -9sin(3x) approaches a value between -9 and 9. Therefore, the limit of sin(3x)/x as x approaches infinity is 0.