If lim(x→0) (sin(3x)/x) = L, what is the value of L?

Core Concept

This is a standard limit that can be evaluated using L'Hôpital's Rule since it's in the indeterminate form 0/0. Differentiating numerator and denominator: lim(x→0) (3cos(3x)/1) = 3cos(0) = 3. Alternatively, recognizing this as a standard limit form: lim(x→0) (sin(ax)/x) = a.