The function $\frac{\sin \left(3 x\right)}{4 x}$ is not defined at $x\=0$ and no amount of factoring or other manipulation can eliminate the "division by zero" issue at $x\=0$. Figure 1.4.1(a) and Table 1.4.1(a) give graphic and numeric evidence that the requisite limit is $3\/4$.

The requisite manipulations are given below. The first equality is valid because $\underset{x\to a}{lim}c f\left(x\right)\=c \underset{x\to a}{lim}f\left(x\right)$, for any nonzero constant $c$. To pass from the second to the third equality, reason that as $x$ goes to zero, so also does $3 x$. Then, to get the fourth equality, set $\mathrm{\θ}\=3 x$.

That Maple can obtain this same result is clear from the calculation $\underset{x\to 0}{lim}\frac{\sin \left(3 x\right)}{4 x}$ = $\frac{3}{4}$.